相关论文: Solution of the nonrelativistic wave equation in t…

This work comes as the second part in a series of investigations into the dynamics of rotating waves as solutions to lattice dynamical systems. Such nonlinear waves as solutions to mathematical equations are of great interest throughout the…

In this paper, we seek to construct nontrivial global solutions to some quasilinear wave equations in three space dimensions. We first present a conditional result on the construction of nontrivial global solutions to a general system of…

We study a family of separable potentials with and without added contact interactions by solving the associated Lippmann-Schwinger equation with two coupled partial waves. The matching of the resulting amplitude matrix with the…

In this paper we prove global regularity for the full water waves system in 3 dimensions for small data, under the influence of both gravity and surface tension. This problem presents essential difficulties which were absent in all of the…

A recursion operator is an integro-differential operator which maps a generalized symmetry of a nonlinear PDE to a new symmetry. Therefore, the existence of a recursion operator guarantees that the PDE has infinitely many higher-order…

A new representation for solutions of Maxwell's equations is derived. Instead of being expanded in plane waves, the solutions are given as linear superpositions of spherical wavelets dynamically adapted to the Maxwell field and…

We present an implementation of the method of orthogonal polynomials which is particularly suitable to study the partition functions of Penner random matrix models, to obtain their explicit forms in the exactly solvable cases, and to…

We consider several models of nonlinear wave equations subject to very strong damping and quasi-periodic external forcing. This is a singular perturbation, since the damping is not the highest order term. We study the existence of response…

The representation of solutions of Maxwell's equations as superpositions of scalar wavelets with vector coefficients developed earlier is generalized to wavelets with polarization, which are matrix-valued. The construction proceeds in four…

Three dimensional nonlinear wave interactions have been analytically described. The procedure under interest can be applied to three dimensional quasilinear systems of first order, whose hydrodynamic reductions are homogeneous…

We obtain exact, simple and very compact expressions for the linearization coefficients of the products of orthogonal polynomials; both the conventional Clebsch-Gordan-type and the modified version. The expressions are general depending…

First, for 3WRI with positive wave energy, we present a regularity theorem for all spatial dimension. Second, for 3WRI with negative wave energy, we present a class of solution in general spatial dimension that will blow up in finite time.…

This study applies the RBF wavelet series to the evaluation of analytical solutions of linear time-dependent wave and diffusion problems of any dimensionality and geometry. To the best of the author's knowledge, such analytical solutions…

We present an alternative method for constructing the exact and approximate solutions of electromagnetic wave equations whose source terms are arbitrary order multipoles on a curved spacetime. The developed method is based on the…

It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…

We show that the isotropic 3-wave kinetic equation is equivalent to the mean field rate equations for an aggregation-fragmentation problem with an unusual fragmentation mechanism. This analogy is used to write the theory of 3-wave…

For a spinless quantum particle in a one-dimensional box or an electromagnetic wave in a one-dimensional cavity, the respective Dirichlet and Neumann boundary conditions both lead to non-degenerate wave functions. However, in two spatial…

We discuss the application of a variant of the method of simplest equation for obtaining exact traveling wave solutions of a class of nonlinear partial differential equations containing polynomial nonlinearities. As simplest equation we use…

In this paper, we first consider the Rosenau equation with the quadratic nonlinearity and identify its Lie symmetry algebra. We obtain reductions of the equation to ODEs, and find periodic analytical solutions in terms of elliptic…

In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…