相关论文: Regular and Singular Pulse and Front Solutions and…
In the present work, we revisit the so-called regularized short pulse equation (RSPE) and, in particular, explore the traveling wave solutions of this model. We theoretically analyze and numerically evolve two sets of such solutions. First,…
In this paper we employ two recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of a recently-derived integrable family of generalized Camassa-Holm (GCH) equations. A recent, novel…
We apply the version of the method of simplest equation called modified method of simplest equation for obtaining exact traveling wave solutions of a class of equations that contain as particular case a nonlinear PDE that models shallow…
We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…
We present a review of our recent works directed towards discovery of a periodic, kink-like and soliton-like travelling wave solutions within the models of transport phenomena and the mathematical biology. Analytical description of these…
We derive a model for the propagation of short pulses in nonlinear media. The model is a higher order regularization of the short pulse equation (SPE). The regularization term arises as the next term in the expansion of the susceptibility…
We investigate the stability of traveling-pulse solutions to the stochastic FitzHughNagumo equations with additive noise. Special attention is given to the effect of small noise on the classical deterministically stable fast traveling…
An analysis of traveling wave solutions of partial differential equation (PDE) systems with cross-diffusion is presented. The systems under study fall in a general class of the classical Keller-Segel models to describe chemotaxis. The…
Traveling modulating pulse solutions consist of a small amplitude pulse-like envelope moving with a constant speed and modulating a harmonic carrier wave. Such solutions can be approximated by solitons of an effective nonlinear Schrodinger…
We consider three novel PDEs associated with the integrable generalizations of the short pulse equation classified recently by Hone {\it et al} (2018 {\it Lett. Math. Phys.} {\bf 108} 927-947). In particular, we obtain a variety of exact…
By using Modified simple equation method, we study the Cahn Allen equation which arises in many scientific applications such as mathematical biology, quantum mechanics and plasma physics. As a result, the existence of solitary wave…
Certain solutions of autonomous PDEs without any boundary conditions describing the spatiotemporal evolution of a dependent variable in an unbounded spatial domain can be characterised as a travelling wave moving with constant speed. In the…
A new method is developed for finding exact solitary wave solutions of a generalized Korteweg-de Vries equation with p-power nonlinearity coupled to a linear Schr\"odinger equation arising in many different physical applications. This…
The solitary wave solution and periodic solutions expressed in terms of elliptic Jacobi's functions are obtained for the nonlinear Schr\"{o}dinger equation governing the propagation of pulses in optical fibers including the effects of…
A nonlinear PDE featuring flux limitation effects together with those of the porous media equation (nonlinear Fokker-Planck) is presented in this paper. We analyze the balance of such diverse effects through the study of the existence and…
We employ the bifurcation theory of planar dynamical systems to investigate the exact travelling wave solutions of a generalized Degasperis-Procesi equation. The implicit expression of smooth soliton solutions is given. The explicit…
The purpose of this work is to introduce a concept of traveling waves in the setting of periodic metric graphs. It is known that the nonlinear Schr{\"o}dinger (NLS) equation on periodic metric graphs can be reduced asymptotically on long…
This paper studies both existence and spectral stability properties of bounded spatially periodic traveling wave solutions to a large class of scalar viscous balance laws in one space dimension with a reaction function of monostable or…
Periodic and solitary travelling-wave solutions of an extended reduced Ostrovsky equation are investigated. Attention is restricted to solutions that, for the appropriate choice of certain constant parameters, reduce to solutions of the…
In this review, we provide a concise summary of several important mathematical results for stochastic travelling waves generated by monostable and bistable reaction-diffusion stochastic partial differential equations (SPDEs). In particular,…