By adding a proper term to the Lagrangian density of a real non-linear KG system with a proposed non-topological unstable solitary wave solution, its stability guaranteed appreciably. This additional term in the new modified Lagrangian density behaves like a strong internal force which stands against any arbitrary small deformation in the proposed non-topological solitary wave solution.

in this work, we successfully construct the new exact traveling wave solutions ofthe generalized sinh–gordon equation by new application of the homogeneousbalance method. the idea introduced in this paper can be applied to othernonlinear evolution equations.

in this paper, the coupled dispersive (2+1)-dimensional long wave equation is studied. the traveling wave hypothesis yields complexiton solutions. subsequently, the wave equation is studied with power law nonlinearity where the ansatz method is applied to yield solitary wave solutions. the constraint conditions for the existence of solitons naturally fall out of the derivation of the soliton so...

In this paper, the coupled dispersive (2+1)-dimensional long wave equation is studied. The traveling wave hypothesis yields complexiton solutions. Subsequently, the wave equation is studied with power law nonlinearity where the ansatz method is applied to yield solitary wave solutions. The constraint conditions for the existence of solitons naturally fall out of the derivation of the soliton so...

in this paper, the coupled dispersive (2+1)-dimensional long wave equation is studied. the traveling wave hypothesis yields complexiton solutions. subsequently, the wave equation is studied with power law nonlinearity where the ansatz method is applied to yield solitary wave solutions. the constraint conditions for the existence of solitons naturally fall out of the derivation of the soliton so...

In this paper, the family of BBM equation with strong nonlinear dispersive B(m,n) equation is introduced. By using a simple and effective algebraic method ,some abundant exact solutions for this class of BBM equations are gotten and call its solutions with solitary patterns, solitary wave solution with singular point , smooth solitary wave solution , kink solution, antikink solution, floating s...

The Jacobin doubly periodic wave solution, the Weierstrass elliptic function solution, the bell-type solitary wave solution, the kink-type solitary wave solution, the algebraic solitary wave solution, and the triangular solution of a generalized Korteweg-de Vries-modified Korteweg-de Vries equation (GKdV-mKdV) with higher-order nonlinear terms are obtained by a generalized subsidiary ordinary d...

Soliton perturbation theory is used to determine the evolution of a solitary wave described by a perturbed nonlinear Schrödinger equation. Perturbation terms, which model wide classes of physically relevant perturbations, are considered. An analytical solution is found for the first-order correction of the evolving solitary wave. This solution for the solitary wave tail is in integral form and ...

The objective of this paper is to study the existence of solitary wave solutions of a fifth order model equation for steady capillary-gravity waves over a bump with the Bond number near 1/3. We proved that there exist solitary wave solutions of the model equation for a sufficiently smooth compact bump. Key-Words: Steady capillary-gravity wave, Solitary wave solution, Compact bump.

The existence of solitary-wave solutions to the three-dimensional water-wave problem with strong surface-tension effects is predicted by the KP-I model equation. The term solitary wave describes any solution which has a pulse-like profile in its direction of propagation, and the KP-I equation admits explicit solutions for three different types of solitary wave. A line solitary wave is spatially...