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1.
Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential 下载免费PDF全文
For the nonlinear wave equation with quartic polynomial potential, bifurcation and solitary waves are investigated. Based on the bifurcation and the energy integral of the two-dimensional dynamical system satisfied by the travelling waves, it is very interesting to find different sufficient and necessary conditions in terms of the bifurcation parameter for the existence and coexistence of bright, dark solitary waves and shock waves. The method of direct integration is developed to give all types of solitary wave solutions. Our method is simpler than other newly developed ones. Some results are similar to those obtained recently for the combined KdV-mKdV equation. 相似文献
2.
HUACun-Cai LIUYan-Zhu 《理论物理通讯》2002,37(1):21-26
Based on the bifurcation and the idea that the solitary waves and shock waves of partial differential equations correspond respectively to the homoclinic and heteroclinic trajectories of nonlinear ordinary differential equations satisfied by the travelling waves,different conditions for the existence of solitary waves of a perturbed sine-Gordon equation are obtained.All of the corresponding approximate solitary wave solutions are given by integrating the derived approximate equations directly. 相似文献
3.
We show that the scattering between two solitary waves in the Fermi-Pasta-Ulam model with interaction potential V (x) = αx^2/2 x^4/4 can be classified into four types according to the configurations of the solitary waves. For three of the four types, the large solitary wave can lose energy and the small one can gain in average by collision.For the other one type in a special parameter region we encounter an anomalous scattering, i.e. the large solitary wave gains energy and the small one loses energy. Numerical investigations are performed for the anharmonic limit case of α = 0 and the general case of α ≠ 0 and comparisons between them are made. 相似文献
4.
HUANG Wen-Hua 《理论物理通讯》2008,50(10):827-831
A general solution including three arbitrary functions is obtained for the (2+1)-dimensional higher-order Broer-Kaup equation by means of WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations. The interactions of the periodic folded waves and their degenerated single folded solitary waves are investigated graphically and are found to be completely elastic. 相似文献
5.
HUANG Wen-Hua 《理论物理通讯》2008,49(6):1383-1388
Applying the extended mapping method via Riccati equation, many exact variable separation solutions for the (2&1 )-dimensional variable coefficient Broer-Kaup equation are obtained. Introducing multiple valued function and Jacobi elliptic function in the seed solution, special types of periodic semifolded solitary waves are derived. In the long wave limit these periodic semifolded solitary wave excitations may degenerate into single semifolded localized soliton structures. The interactions of the periodic semifolded solitary waves and their degenerated single semifolded soliton structures are investigated graphically and found to be completely elastic. 相似文献
6.
The quintic nonlinearity is important in the study of the nonlinear interaction between Langmuir waves and electrons in plasma.Using the pseudoenergy approach,five types of solitary wave solution are obtained explicitly. Only one of these is the modification of the soliton of the cubic nonlinear Schrodinger equation and can be treated perturbatively.However,other four types of solitary wave solution are all induced by the quintic nonlinearity and cannot be treated perturbatively from the solutions of the cubic nonlinear Schrodinger equation. 相似文献
7.
The bifurcations of traveling wave solutions of the Broer–Kaup system are investigated and all possible exact parametric representations of the smooth and peaked solitary waves are presented. 相似文献
8.
Using the wave packet theory,we obtain all the solutions of the weakly damped nonlinear Schrodinger equation.These solutions are the static solution,and solutions of planar wave,solitary wave,shock wave and elliptic function wave and chaos.The bifurcation phenomenon exists in both steady and non-steady solutions.The chaotic and periodic motions can coexist in a certain parametric space region. 相似文献
9.
Application of higher-order KdV——mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere 下载免费PDF全文
Higher-order Korteweg-de Vries (KdV)-modified KdV (mKdV) equations
with a higher-degree of nonlinear terms are derived from a simple
incompressible non-hydrostatic Boussinesq equation set in atmosphere
and are used to investigate gravity waves in atmosphere. By taking
advantage of the auxiliary nonlinear ordinary differential equation,
periodic wave and solitary wave solutions of the fifth-order
KdV--mKdV models with higher-degree nonlinear terms are obtained
under some constraint conditions. The analysis shows that the
propagation and the periodic structures of gravity waves depend on
the properties of the slope of line of constant phase and atmospheric
stability. The Jacobi elliptic function wave and solitary wave
solutions with slowly varying amplitude are transformed into
triangular waves with the abruptly varying amplitude and breaking
gravity waves under the effect of atmospheric instability. 相似文献
10.
YANG Xiao-Xian SHI Yu-Ren DUAN Wen-Shan 《理论物理通讯》2008,49(1):119-122
We discuss the possible nonlinear waves of atomic matter waves in a cigar-shaped Bose-Einstein condensatewith dissipation. The waves can be described by a KdV-type equation. The KdV-type equation has a solitary wave solution. The amplitude, speed, and width of the wave vary exponentially with time t. The dissipative term of ~/ plays an important role for the wave amplitude, speed, and width. Comparisons have been given between the analytical solutions and the numerical results. It is shown that both are in good agreement. 相似文献
11.
Effects of dipole moment on the horizontal dust lattice waves in one-dimensional dust chain are investigated. The general dispersion relations are derived. The waves are sensitive to the direction of the dipole moment, which has an angle θ (0≤ θ≤π) with respect to the vertical direction. When the waves are self-excited, it is shown that the real part of frequency for longitudinal wave is increased, while it is decreased for the horizontal transverse wave with increasing θ. When the waves are externally exited, both the real and imaginary parts of wave number are decreased for the longitudinal and transverse waves with increasing θ. 相似文献
12.
In consideration of adiabatic dust charge variation, the
combined effect of the external magnetized field and the dust
temperature on head-on collision of the three-dimensional dust
acoustic solitary waves is investigated. By using the extended
Poincar\'e--Lighthill--Kuo method, the phase shifts and the
trajectories of two solitons after the collision are obtained. The
effects of the magnitude and the obliqueness of the external
magnetic field and the dust temperature on the
solitary wave collisions are discussed in detail. 相似文献
13.
Exact explicit solitary wave and periodic wave solutions and their dynamical behaviors for the Schamel–Korteweg–de Vries equation 下载免费PDF全文
《中国物理 B》2021,30(6):60201-060201
The Schamel–Korteweg–de Vries equation is investigated by the approach of dynamics.The existences of solitary wave including ω-shape solitary wave and periodic wave are proved via investigating the dynamical behaviors with phase space analyses.The sufficient conditions to guarantee the existences of the above solutions in different regions of the parametric space are given.All possible exact explicit parametric representations of the waves are also presented.Along with the details of the analyses,the analytical results are numerically simulated lastly. 相似文献
14.
A general solution, including three arbitrary functions, is obtained
for a (2+1)-dimensional modified dispersive water-wave (MDWW)
equation by means of the WTC truncation method. Introducing proper
multiple valued functions and Jacobi elliptic functions in the seed
solution, special types of periodic folded waves are derived. In the
long wave limit these periodic folded wave patterns may degenerate
into single localized folded solitary wave excitations. The
interactions of the periodic folded waves and the degenerated
single folded solitary waves are investigated graphically and found
to be completely elastic. 相似文献
15.
Propagation and interaction of ion-acoustic solitary waves in a quantum electron-positron-ion plasma 下载免费PDF全文
This paper discusses the existence of ion-acoustic solitary waves and their interaction in a dense quantum electron-positron-ion plasma by using the quantum hydrodynamic equations.The extended Poincar’e-Lighthill-Kuo perturbation method is used to derive the Korteweg-de Vries equations for quantum ion-acoustic solitary waves in this plasma.The effects of the ratio of positrons to ions unperturbation number density p and the quantum diffraction parameter H e (H p) on the newly formed wave during interaction,and the phase shift of the colliding solitary waves are studied.It is found that the interaction between two solitary waves fits linear superposition principle and these plasma parameters have significantly influence on the newly formed wave and phase shift of the colliding solitary waves.The investigations should be useful for understanding the propagation and interaction of ion-acoustic solitary waves in dense astrophysical plasmas (such as white dwarfs) as well as in intense laser-solid matter interaction experiments. 相似文献
16.
Propagation and Interaction of Ion-Acoustic Solitary Waves in a Two-Dimensional Plasma Consisting of Isothermal Electrons and Hot Ions 下载免费PDF全文
We study the propagation and interaction of ion-acoustic solitary waves in a simple two-dimensional plasma by using the extended Poincare Lighthill-Kuo perturbation method. We consider the interaction between two ion-acoustic solitary waves with different propagation directions in such a system, and obtain two Korteweg-de Vries equations for small but finite amplitude solitary waves along both ξ and η trajectories. The effects of the ratio of ion temperature σ the ratio of heat capacity γ and the colliding angle a on the amplitude, the width of the new nonlinear wave created by the collision between two solitary waves are studied. The effects of these parameters on both the colliding solitary waves are examined as well. It is found that all the above-mentioned parameters have significant effects on the properties of these nonlinear waves. 相似文献
17.
We implement a binary collision approximation to study solitary wave propagation in a two-dimensional double Y-shaped granular chain. The solitary wave was transmitted and reflected when it met the interface of the bifurcated branches of the Y-shaped granular chains. We obtain the analytic results of the ratios of the transmitted and reflected speeds to the incident speed of the solitary wave, the maximum force between the two neighbor beads in a solitary wave, and the total time taken by the pulse to pass through each branch. All of the analytic results are in good agreement with the experimental observations from Daraio et al. [Phys. Rev. E 82 036603 (2010)]. Moreover, we also discuss the delay effects on the arrival of split pulses, and predict the recombination of the split waves traveling in branches in the final stem of asymmetric systems. The prediction of pulse recombination is verified by our numerical results. 相似文献
18.
CHEN Jian-Hong WEI Nan-Xia 《理论物理通讯》2009,51(3):524-528
Taking into account the combined effects of the external magnetic field, adiabatic dust charge fluctuation and collisions occurring between the charged dust grains and neutral gas particles (dust-neutral collisions), the dust-acoustic solitary waves in three-dimensional uniform dusty plasmas are investigated analytically. By using the reductive perturbation method, the Korteweg-de Vries (KdV) equation governing the dnst-aconstic solitary waves is obtained. The present analytical results show that only rarefactive solitary waves exist in this system. It is also found that the effects of the wave vector along the z-direction, dust charge variation, collisional frequency, the plasma density, and temperature ratio can significantly influence the characteristics of low-frequency wave modes. Moreover, for the collisional dusty plasmas, there is a certain critical value μc of the plasma density ratio μ, if μ 〈 μc, the width of the waves increases with μ, otherwise the width of waves decreases with μ. 相似文献
19.
The searching exact solutions in the solitary wave form of non-linear partial differential equations(PDEs play a significant role to understand the internal mechanism of complex physical phenomena. In this paper, we employ the proposed modified extended mapping method for constructing the exact solitary wave and soliton solutions of coupled Klein-Gordon equations and the(2+1)-dimensional cubic Klein-Gordon(K-G) equation. The Klein-Gordon equation are relativistic version of Schr¨odinger equations, which describe the relation of relativistic energy-momentum in the form of quantized version. We productively achieve exact solutions involving parameters such as dark and bright solitary waves, Kink solitary wave, anti-Kink solitary wave, periodic solitary waves, and hyperbolic functions in which severa solutions are novel. We plot the three-dimensional surface of some obtained solutions in this study. It is recognized that the modified mapping technique presents a more prestigious mathematical tool for acquiring analytical solutions o PDEs arise in mathematical physics. 相似文献
20.
《理论物理通讯》2015,(10)
The dissipative nonlinear Schrdinger equation with a forcing item is derived by using of multiple scales analysis and perturbation method as a mathematical model of describing envelope solitary Rossby waves with dissipation effect and external forcing in rotational stratified fluids. By analyzing the evolution of amplitude of envelope solitary Rossby waves, it is found that the shear of basic flow, Brunt–Vaisala frequency and β effect are important factors in forming the envelope solitary Rossby waves. By employing Jacobi elliptic function expansion method and Hirota's direct method, the analytic solutions of dissipative nonlinear Schr¨odinger equation and forced nonlinear Schr¨odinger equation are derived, respectively. With the help of these solutions, the effects of dissipation and external forcing on the evolution of envelope solitary Rossby wave are also discussed in detail. The results show that dissipation causes slowly decrease of amplitude of envelope solitary Rossby waves and slowly increase of width, while it has no effect on the propagation speed and different types of external forcing can excite the same envelope solitary Rossby waves. It is notable that dissipation and different types of external forcing have certain influence on the carrier frequency of envelope solitary Rossby waves. 相似文献