共查询到20条相似文献,搜索用时 654 毫秒
1.
XIAQing-Lin JIANGDong-Chu 《理论物理通讯》2004,42(2):295-298
We introduce a purely anharmonic lattice model with specific double-well on-site potential, which admits traveling compacton-like solitary wave solutions by the inverse method with the help of Mathematica. By properly choosing the shape of the solitary wave solution of the system, we can calculate the parameters of the specific on-site potential. We also found that the localization of the compacton is related to the nonlinear coupling parameter Cn1 and the potential parameter Vo of the on-site potential, and the velocity of the propagation of the compacton is determined by the localization parameter q and the potential parameter Vo. Numerical calculation results demonstrate that the narrow compacton is unstable while the wide compacton is stable when they move along the lattice chain. 相似文献
2.
We study the moving and interaction of the compact-like pulses in the system of an anharmonic lattice with a double well on-site potential by a direct algebraic method and numerical experiments. It is found that the localization of the compact-like pulse is related to the nonlinear coupling parameter Cnl and the potential barrier height V0 of the double well potential. The velocity of the moving compact-like pulse is determined by the linear coupling parameter Cl, the localization parameter q (the nonlinear coupling parameter Cnl) and the potential barrier height Vo.Numerical experiments demonstrate that appropriate Cl is not detrimental to a stable moving of the compact-like pulse.However, the head on interaction of two compact-like pulses in the lattice system with comparatively small Cl leads to the appearance of a discrete stationary localized mode and small amplitude nonlinear oscillation background, while moderate Cl results in the emergence of two moving deformed pulses with damping amplitude and decay velocity and radiating oscillations, and biggish Cl brings on the appearing of four deformed kinks with radiating oscillations and different moving velocities. 相似文献
3.
Bifurcations and Single Peak Solitary Wave Solutions of an Integrable Nonlinear Wave Equation 下载免费PDF全文
Wei Wang Chunhai Li & Wenjing Zhu 《advances in applied mathematics and mechanics.》2016,8(6):1084-1098
Dynamical system theory is applied to the integrable nonlinear wave equation $u_t±(u^3−u^2)x+(u^3)xxx=0$. We obtain the single peak solitary wave solutions and
compacton solutions of the equation. Regular compacton solution of the equation corresponds to the case of wave speed $c$=0. In the case of $c^6$≠0, we find smooth soliton
solutions. The influence of parameters of the traveling wave solutions is explored by
using the phase portrait analytical technique. Asymptotic analysis and numerical simulations
are provided for these soliton solutions of the nonlinear wave equation. 相似文献
4.
XIAQing-Lin YIJian-Hong YETu-Ming DUJuan 《理论物理通讯》2005,44(1):151-154
We study the moving and interaction of the compact-like pulses in the system of an anharmonlc lattice with a double well on-site potential by a direct algebraic method and numerical experiments. It is found that the localization of the compact-like pulse is rClated to the nonlinear coupling parameter Cnl and the potential barrier height Vo of the double well potential. The velocity of the moving compact-like pulse is determined by the linear coupling parameter Cl, the localization parameter q (the nonlinear coupling parameter Cnl) and the potential barrier height Vo.Numerical experiments demonstrate that appropriate Cl is not detrimental to a stable moving of the compact-like pulse.However, the head on interaction of two compact-like pulses in the lattice system with comparatively small Cl leads to the appearance of a discrete stationary localized mode and small amplitude nonlinear oscillation background, while moderate Cl results in the emergence of two moving deformed pulses with damping amplitude and decay velocity and radiating oscillations, and biggish Cl brings on the appearing of four deformed kinks with radiating oscillations and different moving velocities. 相似文献
5.
We study the propagation and collision of the compacton-like kinks in the system of an anharmonic lattice with a double well on-site potential by a direct algebraic method and numerical experiments. It is found that the localization of the compacton-like kinks is related to the nonlinear coupling parameter Cnl and the potential barrier height V0 of the double well potential. The velocity of the propagation of the compacton-like kinks is determined by the linear coupling parameter Cl, the nonlinear coupling parameter Cnl and the localization parameter q. Numerical experiments demonstrate that appropriate Cl is not detrimental to a stable propagation of the compacton-like kinks. However, the collision of compacton-like kinks and anti-kinks in the lattice with comparatively small Cl leads to the emergence of a discrete stationary breather and small amplitude nonlinear oscillation background, while moderate Cl results in the emergence of two deformed kinks with radiating oscillations and lower propagation velocities. 相似文献
6.
New Soliton Solutions with Compact Support for a Family of Two-Parameter Regularized Long-Wave Boussinesq Equations 总被引:1,自引:0,他引:1
YAN ZhenYa 《理论物理通讯》2002,37(6):641-644
Searching for special solitary wave solutions with compact support is of important significance in soliton theory. In this paper, to understand the role of nonlinear dispersion in pattern formation, a family of the regularized longwave Boussincsq equations with fully nonlinear dispersion (simply called R(m, n) equations), utt + a( un )xx + b(um )xxtt = 0(a, b const.), is studied. New solitary wave solutions with compact support of R(m, n) equations are found. In addition we find another compacton solutions of the two special cases, R(2, 2) equation and R(3, 3) equation. It is found that the nonlinear dispersion term in a nonlinear evolution equation is not a necessary condition of that it possesses compacton solutions. 相似文献
7.
Under harmonic approximation, this paper discusses the
linear dispersion relation of the one-dimensional chain. The existence
and evolution of discrete breathers in a general one-dimensional
chain are analysed for two particular examples of soft (Morse) and
hard (quartic) on-site potentials. The existence of discrete
breathers in one-dimensional and two-dimensional Morse lattices is
proved by using rotating wave approximation, local anharmonic
approximation and a numerical method. The localization and amplitude
of discrete breathers in the two-dimensional Morse lattice with on-site
harmonic potentials correlate closely to the Morse parameter a and
the on-site parameter к. 相似文献
8.
《中国物理 B》2018,(12)
Inspired by the recent experimental progress in noisy kicked rotor systems,we investigate the effect of temporal disorder or quasi-periodicity in one-dimensional kicked lattices with pulsed on-site potential.We found that,unlike the spatial disorder or quasi-periodicity which usually leads to localization,the effect of the temporal one is more complex and depends on the spatial configuration.If the kicked on-site potential is periodic in real space,then the wave packet will stay diffusive in the presence of temporal disorder or quasi-periodicity.On the other hand,if the kicked on-site potential is spatially quasi-periodic,then the temporal disorder or quasi-periodicity may lead to a shift of the transition point of the dynamical localization and destroy the dynamical localization in a certain parameter range.The results we obtained can be readily tested by experiments and may help us better understand the dynamical localization. 相似文献
9.
Within a general framework, we discuss the wave function statistics in the Lloyd model of Anderson localization on a one-dimensional lattice with a Cauchy distribution for random on-site potential. We demonstrate that already in leading order in the disorder strength, there exists a hierarchy of anomalies in the probability distributions of the wave function, the conductance, and the local density of states, for every energy which corresponds to a rational ratio of wavelength to lattice constant. Power-law rather than log-normal tails dominate the short-distance wave-function statistics. 相似文献
10.
F. Mancini F. P. Mancini 《The European Physical Journal B - Condensed Matter and Complex Systems》2010,73(4):581-595
We present the exact solution of a system of Fermi particles
living on the sites of a Bethe lattice with coordination number
z and interacting through on-site U and nearest-neighbor V
interactions. This is a physical realization of the extended
Hubbard model in the atomic limit. Within the Green’s function and
equations of motion formalism, we provide a comprehensive
analysis of the model and we study the phase diagram at finite
temperature in the whole model’s parameter space, allowing for the
on-site and nearest-neighbor interactions to be either repulsive
or attractive. We find the existence of critical regions where
charge ordering (V > 0) and phase separation (V < 0) are
observed. This scenario is endorsed by the study of several
thermodynamic quantities. 相似文献
11.
Two-dimensional discrete breathers in a two-dimensional Morse lattice with on-site harmonic potentials are investigated. Under the harmonic approximation, the linear dispersion relations for the triangular and the square lattices are discussed. The existence of discrete breathers in a two-dimensional Morse lattice with on-site harmonic potentials is proved by using local inharmonic approximation and the numerical method. The localization and amplitude of two-dimensional discrete breathers correlate closely to the Morse parameter a and the on-site parameter κ. 相似文献
12.
We have simulated large amplitude motion in cyclic one-dimensional lattices of Morse potential oscillators with a mass impurity, and have observed an unexpected persistence of solitary wave behavior for which we are unable to discover a satisfactory explanation. In solitary wave motion as a function of cycle length and of initial energy, the most common feature of the dynamics is an initial energy plateau with regular oscillatory energy exchange between the solitary wave and other excitations of the lattice, followed by rapid decay. Some systems show no decay at all through 1000 impurity interactions, while others show no significant plateau before decaying. For some cycle lengths there are energy bands in which the solitary wave propagates indefinitely long, with small amplitude oscillatory exchange of energy with the lattice. No regularities were found. 相似文献
13.
YAN Zhen-Ya 《理论物理通讯》2001,(10)
In this paper, similarity rcductions of Boussinesq-like equations with nonlinear dispersion (simply called B(m, n) equations) utt = (un)xx (um) which is a generalized model of Boussinesq equation uts = (u2)xx u and modified Bousinesq equation utt = (u3)xx uxxxx, are considered by using the direct reduction method. As a result,several new types of similarity reductions are found. Based on the reduction equations and some simple transformations,we obtain the solitary wave solutions and compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions, they re-emerge with the same coherent shape) of B(1, n) equations and B(m, m)equations, respectively.`` 相似文献
14.
Zaid M. Odibat 《Physics letters. A》2008,372(8):1219-1227
This Letter deals with compact and noncompact solutions for nonlinear evolution equations with time-fractional derivatives. We present a reliable approach of the homotopy perturbation method to handle nonlinear fractional evolution equations. The validity of the approach is verified through illustrative examples. New exact solitary wave and compacton solutions are developed. The proposed technique could lead to a promising approach for a wide class of nonlinear fractional evolution equations. 相似文献
15.
The spatiotemporal propagation of a momentum excitation on the finite Fermi-Pasta-Ulam lattices is investigated. The competition between the solitary wave and phonons gives rise to interesting propagation behaviors. For a moderate nonlinearity, the initially excited pulse may propagate coherently along the lattice for a long time in a solitary wave manner accompanied by phonon tails. The lifetime of the long-transient propagation state exhibits a sensitivity to the nonlinear parameter. The solitary wave decays exponentially during the final loss of stability, and the decay rate varying with the nonlinear parameter exhibits two different scaling laws. This decay is found to be related to the largest Lyapunov exponent of the corresponding Hamiltonian system, which manifests a transition from weak to strong chaos. The mean-free-path of the solitary waves is estimated in the strong chaos regime, which may be helpful to understand the origin of anomalous conductivity in the Fermi-Pasta-Ulam lattice. 相似文献
16.
K. S. Al-Ghafri 《Waves in Random and Complex Media》2018,28(2):261-269
In this paper, the generalised Klein-Gordon and Kadomtsov–Petviashvili Benjamin–Bona–Mahony equations with power law nonlinearity are investigated. Our study is based on reducing the form of both equations to a first-order ordinary differential equation having the travelling wave solutions. Subsequently, soliton-type solutions such as compacton and solitary pattern solutions are obtained analytically. Additionally, the peaked soliton has been derived where it exists under a specific restrictions. In addition to the soliton solutions, the mathematical method which is exploited in this work also creates a few amount of travelling wave solutions. 相似文献
17.
YAN Zhen-Ya 《理论物理通讯》2001,36(4):385-390
In this paper, similarity reductions of Boussinesq-like equations with nonlinear dispersion (simply called
B(m,n) equations)
utt=(un)xx+(um)xxxx, which is a generalized model of Boussinesq equation utt=(u2)xx+uxxxx and modified Bousinesq equation utt=(u3)xx+uxxxx, are considered by using the direct reduction method. As a result, several new types of similarity reductions are found. Based on the reduction equations and some simple transformations, we obtain the solitary wave solutions and compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions, they re-emerge with
the same coherent shape) of B(1,n) equations and B(m,m) equations,
respectively. 相似文献
18.
In this Letter, the fractional variational iteration method using He?s polynomials is implemented to construct compacton solutions and solitary pattern solutions of nonlinear time-fractional dispersive KdV-type equations involving Jumarie?s modified Riemann-Liouville derivative. The method yields solutions in the forms of convergent series with easily calculable terms. The obtained results show that the considered method is quite effective, promising and convenient for solving fractional nonlinear dispersive equations. It is found that the time-fractional parameter significantly changes the soliton amplitude of the solitary waves. 相似文献
19.
Transient quantum hyperdiffusion, namely, faster-than-ballistic wave packet spreading for a certain time scale, is found to be a typical feature in tight-binding lattices if a sublattice with on-site potential is embedded in a uniform lattice without on-site potential. The strength of the sublattice on-site potential, which can be periodic, disordered, or quasiperiodic, must be below certain threshold values for quantum hyperdiffusion to occur. This is explained by an energy band mismatch between the sublattice and the rest uniform lattice and by the structure of the underlying eigenstates. Cases with a quasiperiodic sublattice can yield remarkable hyperdiffusion exponents that are beyond three. A phenomenological explanation of hyperdiffusion exponents is also discussed. 相似文献
20.
Abundant Symmetries and Exact Compacton—Like Structures in the Two—Parameter Family of the Estevez—Mansfield—Clarkson Equations 总被引:1,自引:0,他引:1
YANZhen-Ya 《理论物理通讯》2002,37(1):27-34
The two-parameter family of Estevez-Mansfield-Clarkson equations with fully nonlinear dispersion (called E(m,n) equations),(uz^m)zzτ γ(uz^nuτ)z uττ=0 which is a generalized model of the integrable Estevez-Mansfield-Clarkson equation uzzzτ γ(uzuzτ uzzuτ) uττ=0,is presented.Five types of symmetries of the E9m,n) equation are obtained by making use of the direct reduction method.Using these obtained reductions and some simple transformations,we obtain the solitary-like wave solutions of E(1,n) equation.In addition,we also find the compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions,they reemerge with the same coherent shape) of E(3,2) equation and E(m,m-1) for its potentials,say,uz,and compacton-like solutions of E(m,m-1) equations,respectively.Whether there exist compacton-like solutions of the other E(m,n) equation with m≠n 1 is still an open problem. 相似文献