This is an announcement of results concerning a class of solitary wave solutions to semilinear wave equations. The solitary waves studied are solutions of the form φ(t, x) = efω(x) to semilinear wave equations such as φ+m2φ = β(|φ|)φ on R1+n and are called nontopological solitons. The first preprint provides a new modulational approach to proving the stability of nontopological solitons. This t...

We study the spectral (in)stability of one-dimensional solitary and cnoidal waves of various Boussinesq systems. These systems model three-dimensional water waves (i.e., the surface is two-dimensional) with or without surface tension. We present the results of numerous computations examining the spectra related to the linear stability problem for both stationary solitary and cnoidal waves with ...

A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. These solitary waves depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the sound speed of the medium. A high-order homogenized model confirms this effective dispersive behavior, and its solutions agree well with those o...

The Gardner equation is an extension of the Korteweg–de Vries (KdV) equation. It exhibits basically the same properties as the classical KdV, but extends its range of validity to a wider interval of the parameters of the internal wave motion for a given environment. In this paper, we derive exact solitary wave solutions for the generalized Gardner equation that includes nonlinear terms of any o...

In this paper,an extended mapping method with symbolic computation is developed to obtain new periodic wave solutions in terms of Jacobin elliptic function for nonlinear evolution equations arising in mathematical physics.As a result,many exact travelling wave solutions are obtained which include new solitary wave solutions,triangular and hyperbolic functions.Solutions in the limiting cases hav...

[1] A sequence of three internal solitary waves of elevation were observed propagating shoreward along a near-bottom density interface over Oregon’s continental shelf. These waves are highly turbulent and coincide with enhanced optical backscatter, consistent with increased suspended sediments in the bottom boundary layer. Nonlinear solitary wave solutions are employed to estimate wave speeds a...

An extended mapping method is used to drive some new exact travelling wave solutions of nonlinear evolution equations arising in physics,namely,generalized Hirota-Satsuma coupled KdV system and coupled Maccaris equations.As a result,many exact travelling wave solutions are obtained which include new solitary wave solutions,triangular and hyperbolic functions.Solutions in the limiting cases have...

We establish exact solutions including periodic wave and solitary wave solutions for the integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota system. We employ this system by using a generalized (G'/G)-expansion and the generalized tanh-coth methods. These methods are developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that these me...

In this paper, we employ the modified simple equation method to find the exact traveling wave solutions involving parameters of nonlinear evolution equations via the (1+1)dimensional generalized shallow water-wave equation and the(2+1)-dimensional KdV-Burgers equation. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave sol...

We prove existence and stability results for a two-parameter family of solitary-wave solutions to a system in which an equation of nonlinear Schrödinger type is coupled to an equation of Korteweg-de Vries type. Such systems model interactions between short and long dispersive waves. The results extend earlier results of Angulo, Albert and Angulo, and Chen. Our proof involves the characterizatio...