相关论文: Solutions of Jimbo-Miwa Equation and Konopelchenko…

Coupled Boussinesq equations describe long weakly-nonlinear longitudinal strain waves in a bi-layer with a soft bonding between the layers (e.g. a soft adhesive). From the mathematical viewpoint, a particularly difficult case appears when…

The classical wave equation in the space of generalized functions (distributions)is considered. The Distributions Method of building the solutions of nonstationary boundary value problems (NBVP) for wave equations in coordinates spaces of…

We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…

In this technical note, we consider the stability properties of a viscously damped Timoshenko beam equation with spatially varying parameters. With the help of the port-Hamiltonian framework, we first prove the existence of solutions and…

All complex fluid motions, such as transition and turbulence, obeying the Navier-Stokes equations are non-linear phenomena. Some aspects of the non-linear terms of these equations are not well understood and are, in fact, misunderstood. The…

This paper provides an alternative methodology for analysis of three-wave interactions under the exact dispersion relation associated with gravity waves in fluid of intermediate depth. A Korteweg-de Vries type of equation with exact…

We present a dissipative algorithm for solving nonlinear wave-like equations when the initial data is specified on characteristic surfaces. The dissipative properties built in this algorithm make it particularly useful when studying the…

Lump solutions are spatially rationally localized solutions which usually arise as solutions to higher dimensional nonlinear partial differential equations often possessing Hirota bilinear forms. Under some parameter constraint, these…

We establish the existence theory of several commonly used finite element (FE) nonlinear fully discrete solutions, and the convergence theory of a linearized iteration. First, it is shown for standard FE, SUPG and edge-averaged method…

The Benjamin-Bona-Mahony (BBM) equation has proven to be a good approximation for the unidirectional propagation of small amplitude long waves in a channel where the crosswise variation can be safely ignored. The…

The Smoluchowski equation is a system of partial differential equations modelling the diffusion and binary coagulation of a large collection of tiny particles. The mass parameter may be indexed either by positive integers, or by positive…

The Hirota equation is a higher order extension of the nonlinear Schroedinger equation by incorporating third order dispersion and one form of self steepening effect. New periodic waves for the discrete Hirota equation are given in terms of…

We construct the solution of the Riemann problem for the shallow water equations with discontinuous topography. The system under consideration is non-strictly hyperbolic and does not admit a fully conservative form, and we establish the…

We consider co-rotational wave maps from the $(1+d)$-dimensional Minkowski space into the $d$-sphere for $d\geq 3$ odd. This is an energy-supercritical model which is known to exhibit finite-time blowup via self-similar solutions. Based on…

We revisit some issues about existence and regularity for the wave equation in noncylindrical domains. Using a method of diffeomorphisms, we show how, through increasing regularity assumptions, the existence of weak solutions, their…

In this paper we introduce a new property of two-dimensional integrable systems -- existence of infinitely many local three-dimensional conservation laws for pairs of integrable two-dimensional commuting flows. Infinitely many…

In this note we present a new KAM result which proves the existence of Cantor families of small amplitude, analytic, quasi-periodic solutions of derivative wave equations, with zero Lyapunov exponents and whose linearized equation is…

We study the stability of steady-state solutions of the Wave-Kinetic Equations for acoustic waves. Combining theoretical analysis and numerical simulations, we characterise the time evolution of small isotropic perturbations for both 2D and…

Reductions of the KP-Whitham system, namely the (2+1)-dimensional hydrodynamic system of five equations that describes the slow modulations of periodic solutions of the Kadomtsev-Petviashvili (KP) equation, are studied. Specifically, the…

Local solutions of the static, spherically symmetric Einstein-Yang-Mills (EYM) equations with SU(2) gauge group are studied on the basis of dynamical systems methods. This approach enables us to classify EYM solutions in the origin…