and Applied Analysis 3 25 , the traveling wave solution of 1.2 is a damped oscillatory solution which has a bell profile head. However, they did not present any analytic solution or approximate solution for 1.2 . Xiong 25 obtained a kink profile solitary wave solution for KdV-Burgers equation. In 26 , S. D. Liu and S. D. Liu obtained an approximate damped oscillatory solution to a saddle-focus ...

A strongly nonlinear asymptotic model describing the evolution of large amplitude internal waves in a two-layer system is studied numerically. While the steady model has been demonstrated to capture correctly the characteristics of large amplitude internal solitary waves, a local stability analysis shows that the time-dependent inviscid model suffers from the Kelvin-Helmholtz instability due to...

We consider the logarithmic Korteweg–de Vries (log–KdV) equation, which models solitary waves in anharmonic chains with Hertzian interaction forces. By using an approximating sequence of global solutions of the regularized generalized KdV equation in H(R) with conserved L norm and energy, we construct a weak global solution of the log–KdV equation in a subset of H(R). This construction yields c...

Simulation of free surface flow and sudden wave profile are recognized as the most challenging problem in computational hydraulics. Several Eulerian/Lagrangian approaches and models can be implemented for simulating such phenomena in which the smoothed particle hydrodynamics method (SPH) is categorized as a proper candidate. The incompressible SPH (ISPH) method hires a precise incompressible hy...

We consider the negative order KdV (NKdV) hierarchy which generates nonlinear integrable equations. Selecting different seed functions produces evolution apply traveling wave setting to study one of these Assuming a particular type solution leads us solve cubic equation. New solutions are found, but none classical solitary solutions.

Solitary wave is a permanent when the dissipation ignored. Many analytical solutions have been developed for finite amplitude solitary waves. In additional to perturbation solutions, closed form are also available (e.g., McCowan 1891, Clamond and Fructus 2003, being denoted as CF from hereon), which more accuracy, especially larger waves were discussed in Wang Liu (2022). (2022) ’s laboratory e...

– We present the theory and the experimental observation of break-up of twodimensional bright spatial solitons propagating in a three-dimensional bulk photorefractive nonlinear medium due to transverse modulation instability. Solitary wave (self-bound) solutions of nonlinear propagation equations are a fascinating topic of nonlinear dynamics. The analysis of their stability and nonlinear evolut...

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...

We consider the half-wave equation with mass critical in two dimensions {iut=Du?|u|u, u(t0,x)=u0(x), First, we prove existence of a family traveling solitary waves. then show finite-time blowup solutions ground state ?u0?2=?Q?2, where Q is solution DQ+Q=Q2.