We present new periodic, kink-like and soliton-like travelling wave solutions to the hyperbolic generalization of Burgers equation. To obtain them, we employ the classical and generalized symmetry methods and the ansatz-based approach

Orbital and asymptotic stability for 1-soliton solutions to the Toda lattice equations as well as small solitary waves to the FPU lattice equations are established in the energy space. Unlike analogous Hamiltonian PDEs, the lattice equations do not conserve momentum. Furthermore, the Toda lattice equation is a bidirectional model that does not fit in with existing theory for Hamiltonian system ...

Many new solitary wave solutions of the recently studied Lienard equation are obtained by mapping it to the field equation of the φ6−field theory. Further, it is shown that the exact solutions of the Lienard equation are also the exact solutions of the various perturbed soliton equations. Besides, we also consider a one parameter family of generalised Lienard equations and obtain exact solitary...

By using the integral bifurcation method, we study the nonlinearK m,n equation for all possible values of m and n. Some new exact traveling wave solutions of explicit type, implicit type, and parametric type are obtained. These exact solutions include peculiar compacton solutions, singular periodic wave solutions, compacton-like periodic wave solutions, periodic blowup solutions, smooth soliton...

We study quadratic solitons supported by two- and three-wave parametric interactions in chi((2)) nonlinear media. Both planar and two-dimensional cases are considered. We obtain very accurate, "almost exact," explicit analytical solutions, matching the actual bright soliton profiles, with the help of a specially developed approach, based on analysis of the scaling properties. Additionally, we u...

We construct the traveling wave solutions of the 1 1 -dimensional modified Benjamin-BonaMahony equation, the 2 1 -dimensional typical breaking soliton equation, the 1 1 -dimensional classical Boussinesq equations, and the 2 1 -dimensional Broer-Kaup-Kuperschmidt equations by using an extended G′/G -expansion method, where G satisfies the second-order linear ordinary differential equation. By us...

Keywords: (3 + 1)-dimensional Jimbo–Miwa equation Hirota bilinear form Wronskian determinant solution a b s t r a c t In this paper, we obtain two kinds of sufficient conditions consisting of systems of linear partial differential equations, which guarantee that the corresponding Wroskian determinant solves the (3 + 1)-dimensional Jimbo–Miwa equation in the Hirota bilinear form. Our results sug...

The interactions between soliton solutions of integrable models are usually considered to be completely elastic. That is to say, the amplitude, velocity and wave shape of solitons are not changed after nonlinear interaction [1]. However, for some specific solutions of some (2+1)-dimensional models, the interactions among solitonic excitations are not completely elastic since their shapes are ch...

Many physical phenomena are modeled with nonlinear partial differential equations that possess solitary wave solutions called solitons. Solitons exhibit Gaussian forms and in turn engender normal probability distributions. Moreover, solitons fluctuate randomly during evolution. These features intricately relate the solitons to wavelets, statistical distributions and random processes. In the pre...