Related papers: Weak asymptotics method
We consider evolution of wave pulses with formation of dispersive shock waves in framework of fully nonlinear shallow-water equations. Situations of initial elevations or initial dips on the water surface are treated and motion of the…
A system of quasilinear elliptic equations on an unbounded domain is considered. The existence of a sequence of radially symmetric weak solutions is proved via variational methods.
In this paper, we use Hirota's bilinear method to directly construct periodic wave solutions of nonlinear equations. The asymptotic property of periodic wave solutions are analyzed. It is shown that well-known soliton solutions can be…
We review the recent developments of the use of the homotopy method for solving the non-linear evolution equation for the diffractive production in deep inelastic scattering. We introduce part of the non-linear corrections in the linear…
In this paper, we consider the wave propagations of viscoelastic materials, which has been derived by Taiping-Liu to approximate the viscoelastic dynamic system with fading memory (see [T.P.Liu(1988)\cite{LiuTP}]) by the Chapman-Enskog…
This course introduces the use of semigroup methods in the solution of linear and nonlinear (quasi-linear) hyperbolic partial differential equations, with particular application to wave equations and Hermitian hyperbolic systems. Throughout…
The coordinate asymptotics of the wave function for the problem of scattering of three particles with Coulomb interaction is constructed. Representation of hyperspherical functions is used to reduce the Schr\"odinger equation to a system of…
We propose a systemic method of applying the auxiliary systems of original equations to find the high order nonlocal symmetries of nonlinear evolution equation. In order to validate the effectiveness of the method, some examples are…
This paper presents a new technique to calculate the evolution of a quantum wavefunction in a chosen spatial basis by minimizing the accumulated action. Introduction of a finite temporal basis reduces the problem to a set of linear…
A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…
Based on the known implicit solution for nonlinear plasma waves, an explicit solution was obtained in the form of decomposition into harmonics. The solution obtained exhibits a mechanism for steepening of nonlinear plasma wave as a result…
We consider the coupled electromagnetic waves propagating in a waveguide array, which consists of alternating waveguides of positive and negative refraction indexes. Due to zigzag configuration there are interactions between both nearest…
In this short note, we derive a system of two nonlocal equations for the water-wave problem following the work of [AFM06]. Specifically, we consider a fluid with a one-dimensional free surface for an irrotational fluid both with, and…
In this paper, we propose a new asymptotic expansion approach for nonlinear filtering based on a small parameter in the system noise. This method expresses the filtering distribution as a power series in the noise level, where the…
We present a new and relatively elementary method for studying the solution of the initial-value problem for dispersive linear and integrable equations in the large-$t$ limit, based on a generalization of steepest descent techniques for…
Sampling equation method is presented to look for exact solutions of nonlinear differential equations. Application of this approach to one of the extensive chaos model is considered. Exact solutions of this model in travelling wave are…
We present a mechanism to generate unidirectional pulse-shaped propagating waves, tamed to exponential growth and dispersion, in active systems with nonreciprocal and nonlinear couplings. In particular, when all bulk modes are exponentially…
This paper addresses the existence of nonnegative mild solutions for stochastic evolution inclusions through a weak topology approach. Precisely, the study focuses on stochastic evolution inclusions characterized by multivalued…
This paper deals with the exact solutions of a nonlinear coupled coupled wave equation. The (G'/G)-expansion method has been applied to derive kink solutions and singular wave solutions. The restrictions on the coefficients of the governing…
We present a method for finding the asymptotics of integrals arising in solid mechanics.