Solution of the nonlinear Klein-Gordon equation perturbed by small external force is investigated. The frequency of perturbation varies slowly and passes through a resonance. The resonance generates a solitary packets of waves. Full asymptotic description of this process is presented. Introduction This work is devoted to the problem on a generation of solitary packets of waves by a small extern...

This study investigates exact analytical solutions of some nonlinear partial differential equations arising in mathematical physics. To this reason, the Kudryashov-Sinelshchikov equation, ZK-BBM equation and Gardner have been considered. With implementation trial solution algorithm, solitary wave, bright, dark periodic traveling wave considered attained. The checked graphs given via package pro...

In this paper, a closed form optical soliton solution is obtained for the nonlinear Schrödinger’s equation with fourth order dispersion in a Kerr law media. The solitary wave ansatze is used to carry out the integration of this equation. Finally, a numerical simulation is given for the closed form soliton solution. Mathematics Subject Classification: 35Q51, 35Q53, 37K10, 78A60 PACS Codes: 02.30...

Solitary wave interaction for a higher-order modified Korteweg-de Vries (mKdV) equation is examined. The higher-order mKdV equation can be asymptotically transformed to the mKdV equation, if the higher-order coefficients satisfy a certain algebraic relationship. The transformation is used to derive the higher-order two-soliton solution and it is shown that the interaction is asymptotically elas...

An alternative type of nonlinear evolution equation is derived that describes interfacial waves in a two-layer fiuid system. The equation presented here is a higher-order version of the Benjamin-Ono (BO) equation. A solitary-wave solution of the equation is obtained by means of a singular perturbation method. The characteristics of the solution are discussed in comparison with those for a highe...

In this paper, we obtained the 1-soliton solutions of the symmetric regularized long wave (SRLW) equation and the (3+1)-dimensional shallow water wave equations. Solitary wave ansatz method is used to carry out the integration of the equations and obtain topological soliton solutions The physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. Note t...

We consider a weakly dissipative hyperelastic-rod wave equation (or weakly dissipative Camassa–Holm equation) describing nonlinear dispersive dissipative waves in compressible hyperelastic rods. By fixed a smooth solution, we establish the existence of a strongly continuous semigroup of global weak solutions for any initial perturbation from H1(R). In particular, the supersonic solitary shock w...

This paper focuses on applying the GDTM-Padé technique to solve the non-linear differential-difference equation. The bell-shaped solitary wave solution of Belov-Chaltikian lattice equation is considered. Comparison between the approximate solutions and the exact ones shows that this technique is an efficient and attractive method for solving the differential-difference equations.

Consider the focusing mass-critical nonlinear Hartree equation iut + u=−(| · |−2 ∗ |u|2)u for spherically symmetric H 1 x initial data with ground state mass M(Q) in dimension d 5. We show that any global solution u which does not scatter must be the solitary wave eitQ up to phase rotation and scaling. © 2008 Elsevier Inc. All rights reserved. MSC: 35Q55

Based on the traveling wave reduction method with a perturbed initial solution and F-expansion method, class of explicit exact solutions (2+1)-dimensional CDGKS equation are obtained through symbolic computation. Moreover, both interaction behavior between parameters perturbation degree periodic Gauss to rational pulse wave, correlation superposition energy solitary discussed. Finally, numerica...