This paper examines the generation and propagation of a Third order solitary water wave along the channel. First the Incompressible Smoothed Particle Hydrodynamics (ISPH) numerical method is described and the boundary condition handling method is presented. The numerical model is then used to simulate solitary wave propagation along the fixed depth channel. The numerical results are compared wi...

The travelling wave problem for a particular bidirectional Whitham system modelling surface water waves is under consideration. This firstly appeared in Dinvay et al. (2019), where it was numerically shown to be stable and good approximation the incompressible Euler equations. In subsequent papers (Dinvay, 2019; al., 2019) initial-value studied well-posedness classical Sobolev spaces proved. He...

We have found exact, periodic, time-dependent solitary wave solutions of a discrete 4 field theory model. For finite lattices, depending on whether one is considering a repulsive or attractive case, the solutions are Jacobi elliptic functions, either sn x ,m which reduce to the kink function tanh x for m→1 , or they are dn x ,m and cn x ,m which reduce to the pulse function sech x for m→1 . We ...

By means of the coupled amplitude-phase method we find analytical dark solitary wave solutions for the higher order nonlinear Schrödinger equation with cubic-quintic terms describing the effects of quintic nonlinearity on the ultra-short (femtosecond) optical soliton propagation in non-Kerr media. The dark solitary wave solution exists even for the coefficients of quintic terms much larger than...

An integrable 2-component Camassa-Holm 2-CH shallow water system is studied by using integral bifurcation method together with a translation-dilation transformation. Many traveling wave solutions of nonsingular type and singular type, such as solitary wave solutions, kink wave solutions, loop soliton solutions, compacton solutions, smooth periodic wave solutions, periodic kink wave solution, si...

We have found exact, periodic, time-dependent solitary wave solutions of a discrete φ field theory model. For finite lattices, depending on whether one is considering a repulsive or attractive case, the solutions are either Jacobi elliptic functions sn(x,m) (which reduce to the kink function tanh(x) for m → 1), or they are dn(x,m) and cn(x,m) (which reduce to the pulse function sech(x) for m → ...