Related papers: Group classification of nonlinear wave equations
The method of nonlinear realizations is a convenient tool for building dynamical realizations of a Lie group, which relies solely upon structure relations of the corresponding Lie algebra. The goal of this work is to discuss advantages and…
We give the classification of T-duals of the flat background in four dimensions with respect to one-, two-, and three-dimensional subgroups of the Poincar\'e group using non-Abelian T-duality with spectators. As duals we find backgrounds…
We consider the two-dimensional quasilinear wave equations with quadratic nonlinearities. We introduce a new class of null forms and prove uniform boundedness of the highest order norm of the solution for all time. This class of null forms…
A unified treatment is given of low-weight modular forms on \Gamma_0(N), N=2,3,4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations,…
In this paper, we use the equivariant degree theory to establish a global bifurcation result for the existence of non-stationary branches of solutions to a nonlinear, two-parameter family of hyperbolic wave equations with local delay and…
We study the application of generalized symmetry for reducing nonlinear partial differential equations. We construct the ansatzes for dependent variable $u$ which reduce the scalar partial differential equation with two independent…
The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions,…
Given a class of differential equations with arbitrary element, the problems of symmetry group, nonclassical symmetry and conservation law classifications are to determine for each member the structure of its Lie symmetry group, conditional…
We consider a class of (1+2)-dimensional linear partial differential of Asian options pricing. Special cases have been used to models of financial mathematics. We carry out group classification of a class equations. In particular, the…
The complete group classification problem for the class of (1+1)-dimensional $r$th order general variable-coefficient Burgers-Korteweg-de Vries equations is solved for arbitrary values of $r$ greater than or equal to two. We find the…
We investigate the integrability of a class of 1+1 dimensional models describing nonlinear dispersive waves in continuous media, e.g. cylindrical compressible hyperelastic rods, shallow water waves, etc. The only completely integrable cases…
We show that a general class of quasilinear wave equations have global solutions for small initial data as we conjectured in an earlier paper.
The well-known 5-parameter isometry group of plane gravitational waves in $4$ dimensions is identified as Levy-Leblond's Carroll group in $2+1$ dimensions with no rotations. Our clue is that plane waves are Bargmann spaces into which…
Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links…
We consider semilinear wave equations with small initial data in two space dimensions. For a class of wave equations with cubic nonlinearity, we show the global existence of small amplitude solutions, and give an asymptotic description of…
A combination of some weighted energy estimates is applied for the Cauchy problem of quasilinear wave equations with the standard null conditions in three spatial dimensions. Alternative proofs for global solutions are shown including the…
The algebraic method for computing the complete point symmetry group of a system of differential equations is extended to finding the complete equivalence group of a class of such systems. The extended method uses the knowledge of the…
We establish that solutions, to the most simple NLKG equations in 2 space dimensions with mass resonance, exhibits long range scattering phenomena. Modified wave operators and solutions are constructed for these equations. We also show that…
Surface water waves in ideal fluids have been typically modeled by asymptotic approximations of the full Euler equations. Some of these simplified models lose relevant properties of the full water wave problem. One of them is the Galilean…
This paper addresses the inverse problem of simultaneously recovering multiple unknown parameters for semilinear wave equations from boundary measurements. We consider an initial-boundary value problem for a wave equation with a general…