Related papers: Wave Solutions
The approach allowing is considered to represent the solutions such as stationary lonely waves of various nonlinear wave the equations as system of the ordinary differential equations in variable action - angle.
This paper studies the upper bound of the lifespan of classical solutions of the initial value problems for one dimensional wave equations with quasilinear terms of space-, or time-derivatives of the unknown function. The results are same…
We prove wave breaking --- bounded solutions with unbounded derivatives --- in the nonlinear nonlocal equation which combines the dispersion relation of water waves and a nonlinearity of the shallow water equations, provided that the slope…
In quantum theory particles are represented as wave packets. Shock wave analysis of quantum equations of motion shows that wave function representation in general and wave packet description in particular contains discontinuities due to a…
This article produces wave equations and constructs traveling wave solutions that are intimately related to Newton's equations of celestial mechanics. The traveling wave solutions are expressed in ``closed form'' in terms of elementary…
The generalized equation for the study of two-component nonlinear waves in different fields of physics is considered. In special cases, this equation is reduced to a set of the various well-known equations describing nonlinear solitary…
We consider wave equations on Lorentzian manifolds in case of low regularity. We first extend the classical solution theory to prove global unique solvability of the Cauchy problem for distributional data and right hand side on smooth…
The objective of this paper is to construct geometrically Riemann $k$-wave solutions of the general form of first-order quasilinear hyperbolic systems of partial differential equations. To this end, we adapt and combine elements of two…
We numerically study nonlinear phenomena related to the dynamics of traveling wave solutions of the Serre equations including the stability, the persistence, the interactions and the breaking of solitary waves. The numerical method utilizes…
A method based off of operator consideration for solving the time evolution of a wave function is developed. The method is applied to free space, constant force and harmonic oscillator potentials where general solutions are derived for the…
Wilton ripples are a type of periodic traveling wave solution of the full water wave problem incorporating the effects of surface tension. They are characterized by a resonance phenomenon that alters the order at which the resonant harmonic…
We construct solutions to nonlinear wave equations that are singular along a prescribed noncharacteristic hypersurface which is the graph of a function satisfying not the Eikonal but another partial differential equation of the first order.…
Complete analysis of quantum wave functions of linear systems in an arbitrary number of dimensions is given. It is shown how one can construct a complete set of stationary quantum states of an arbitrary linear system from purely classical…
We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed…
The wave turbulence equation is an effective kinetic equation that describes the dynamics of wave spectrum in weakly nonlinear and dispersive media. Such a kinetic model has been derived by physicists in the sixties, though the…
Some higher-order quasilinear parabolic, hyperbolic, and nonlinear dispersion equations are shown to admit various blow-up, extinction, and travelling wave solutions, which reduce to variational problems admitting countable families of…
The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators.…
Third-order approximate solutions for surface gravity waves in the finite water depth are studied in the context of potential flow theory. This solution provides explicit expressions for the surface elevation, free-surface velocity…
The goal of this work is to determine classes of travelling solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz. It is shown that spurious solitary waves can occur in…
The Westervelt equation describes the propagation of pressure waves in continuous nonlinear and, eventually, diffusive media. The classical framework of this equation corresponds to fluid dynamics theory. This work seeks to connect this…