Spatiotemporal solitons on cnoidal wave backgrounds in three media with different distributed transverse diffraction and dispersion

The (3+1)-dimensional nonlinear Schrödinger equation with different distributed transverse diffraction and dispersion is studied based on the similarity transformation, and exact bright soliton solution on cnoidal wave backgrounds is derived. Moreover, three kinds of dynamical behaviors of these soliton solutions in three different dispersion/diffraction decreasing media with the Gaussian, hyperbolic, and Logarithmic profiles are discussed. Solitons interact with cnws and/or the change of characteristics of solitons by an addition of cnws are studied. Result of comparison with three media indicates that for the same parameters, the bright soliton in the Gaussian profile is compressed to the utmost degree. These results are potentially useful for future experiments in the optical communications, long-haul telecommunication networks, and Bose–Einstein condensations.     

Three-dimensional vector solitons and their stabilities in a Kerr medium with spatially inhomogeneous nonlinearity and transverse modulation

Nonlinear Dynamics - Analytical vector spatiotemporal soliton solutions are derived in a spatially inhomogeneous Kerr nonlinear medium with a transverse modulation by means of a generic...     

Damping of solitons in bubble media

The author considers the problem of damping of solitons in a bubble medium because of viscosity and interphase heat and mass transfer nonequilibrium on the assumption that their evolution is described by successive interchange of steady soliton solutions. The changes in the amplitude of the solitons obtained from analytical expressions are compared with the available experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 52–61, July–August, 1987.     

Parametric interaction of acoustic waves in micro-inhomogeneous media with hysteretic nonlinearity and relaxation

A theoretical investigation of parametric processes that arise as a result of the interaction of powerful and weak longitudinal acoustic waves in micro-inhomogeneous media with hysteretic nonlinearity and relaxation was carried out. The case of degenerate interaction between a powerful high-frequency wave and a weak low-frequency one was considered. The nonlinear damping coefficient and the carrier frequency phase delay of the weak wave propagating under the action of the powerful wave were determined.     

Stable localized spatial solitons in \mathcal {PT}-symmetric potentials with power-law nonlinearity

We derive analytical spatial soliton solutions of a (2 + 1)-dimensional nonlinear Schrödinger equation with power-law nonlinearity in \(\mathcal {PT}\) -symmetric potentials. The stability of these solutions is tested by the linear stability analysis and the direct numerical simulations. Moreover, some dynamical characteristics of these solutions, such as the phase switch, the power, and the transverse power-flow density, are also examined.     

Modulational instability of gap solitons in single-walled carbon nanotube lattices

Modulational instability and nonlinear localized excitations are addressed, in the framework of a one-dimensional diatomic carbon nanotube (CNT) model, using the quasi-discrete approximation. Gap soliton solutions, based on the modulational instability criterion, are studied, where one considers the solutions arising in the upper and lower optical frequency cutoff regimes, and in the upper acoustic frequency cutoff mode. Solutions are found as breathers and double breathers, and their response to interatomic interaction parameters is discussed. Vibrations of the CNTs from the two modes are compared based on their capability of carrying the amount of energy required for specific purposes, either in Microelectronics or in Nano-devices.     

High-order revivable complex-valued hyperbolic-sine-Gaussian solitons and breathers in nonlinear media with a spatial nonlocality

In this paper, based on the nonlocal nonlinear Schrödinger equation, the evolution of complex-valued hyperbolic-sine-Gaussian beams (CVHSGBs) is investigated in nonlinear media with a spatial nonlocality. It is found that the evolution of CVHSGBs is variable depending on the parameters of complex-valued hyperbolic sine function. Choosing special parameters, the pattern of CVHSGBs can keep unchanged during propagation, and they propagate as solitons or breathers. Furthermore, for the general case, the CVHSGB evolutes periodically, and it recovers into its initial pattern at the end of each evolution period, namely it can be revivable periodically, which can be regarded as a generalized high-order breather. A series of analytical expressions are derived to describe the beam evolution, the intensity pattern, the beam spot size, the real beam curvature, etc. Some numerical simulations are also performed to demonstrate the typical evolution properties.     

A new equation and exact solutions describing focal fields in media with modular nonlinearity

Nonlinear Dynamics - Brand-new equations which can be regarded as modifications of Khokhlov–Zabolotskaya–Kuznetsov or Ostrovsky–Vakhnenko equations are suggested. These equations...     

On the theory of three-dimensional multihump solitons in active-dissipative media

Stable localized nonlinear coherent structures, i.e. solitons, play a key role in the stochastization of the processes occurring in active-dissipative media. In this study, three-dimensional multi-hump solitons are investigated for a model equation which qualitatively describes the wave processes in some physical systems. The existence of 3D multihump solitons is demonstrated numerically and the soliton behavior is studied. The results are generalized to describe multihump solitons in descending viscous-fluid layers [1]. An unusual physical phenomenon observed in experiments [1], namely, stable two-hump coherent structures on the surface of a downflowing viscous-fluid layer, is explained qualitatively.     

Numerical simulation of standing solitons and their interaction

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Stable and oscillating solitons of $$pmb {mathcal {PT}}$$ -symmetric couplers with gain and loss in fractional dimension

Nonlinear Dynamics - Families of coupled solitons of $$mathcal {PT}$$ -symmetric physical models with gain and loss in fractional dimension and in settings with and without cross-interactions...     

Dark and gray solitons of ($$$$)-dimensional nonlocal nonlinear media with periodic response function

By using the standard symmetry reduction method, some exact analytical solutions including gray solitons and gray soliton lattice solutions are derived for the (\(2+1\))-dimensional nonlinear optical media with periodic nonlocal response. Furthermore, dark/gray soliton solutions and dark soliton lattice solutions are found by means of hyperbolic function expansion method and elliptic function expansion method for the nonlocal nonlinear system, respectively. It is found that two critical points exist for soliton solutions, and the switching dynamics of solitons may be described by the critical points.     

Existence and stability of traveling waves in periodic media governed by a bistable nonlinearity

We prove the existence of multidimensional traveling wave solutions of the bistable reaction-diffusion equation with periodic coefficients under the condition that these coefficients are close to constants. In the case of one space dimension, we prove their asymptotic stability.     

Plane waves in nonhomogeneous plastic media and their interaction with obstacles

Media in which the propagation of strong disturbances is usually studied are in many cases nonhomogeneous.     

Accurate and straightforward symplectic approach for fracture analysis of fractional viscoelastic media

An accurate and straightforward symplectic method is presented for the fracture analysis of fractional two-dimensional(2D) viscoelastic media. The fractional Kelvin-Zener constitutive model is used to describe the time-dependent behavior of viscoelastic materials. Within the framework of symplectic elasticity, the governing equations in the Hamiltonian form for the frequency domain(s-domain) can be directly and rigorously calculated. In the s-domain, the analytical solutions of the displacement ...     

Three-dimensional optical solitons formed by the balance between different-order nonlinearities and high-order dispersion/diffraction in parity-time symmetric potentials

Nonlinear Dynamics - Under parity-time symmetric potentials, different-order nonlinearities such as cubic, quintic and septimal nonlinearities, altogether with their combinations and second-order...