1 General solution to wave equationPropagation, Wave
u ∂η = a 2 ∂ 2 u ∂ξ 2 −2a 2 ∂ 2 u ∂ξ∂η +a 2 ∂ 2 u ∂η 2 Then 0 = a 2 u xx −u tt = 4a 2 ∂ 2 u ∂ξ∂η And therefore the wave equation (1) transforms into u ξη = 0. It is easy to find the general solution to this...
A general solution is given for a fractional diffusion-wave equation defined in a bounded space domain. The fractional time derivative is described in the Caputo sense. The finite sine transform technique is used to convert a fractional differential equation from a space domain to a wavenumber doma...
An entire solution of the Allen-Cahn equation $\\Delta u=f(u)$, where $f$ is an odd function and has exactly three zeros at $\\pm 1$ and $0$, e.g. $f(u)=u(... F Pacard,Y Liu,M Kowalczyk - 《Networks & Heterogeneous Media》 被引量: 127发表: 2012年 General decay rates...
In this paper we prove the existence of solution and uniform decay of energy to the mixed problem for coupled wave equation of Kirchhoff-type subject to me... JJ Bae - 《Nonlinear Analysis》 被引量: 34发表: 2005年 Time decay of solutions to degenerate Kirchhoff type equation In this paper...
The most general solution to this equation can be written in the form: (64)p=f1x+ct+f2x−ct This solution consists of two free traveling waves moving in opposite directions. VI.B Standing Waves Consider the waves described immediately above, but limit the discussion to harmonic motion of ...
We extend this study to a more general nonlinear equation, which is the general Korteweg–De-Vries (GKDV) equation, in which the previous studies is a special case of it. The method applied here is Adomian decomposition method, which has been developed by George Adomian [Solving Frontier ...
Analytical solution for the space fractional diffusion equation by two-step Adomian Decomposition Method 2009, Communications in Nonlinear Science and Numerical Simulation Citation Excerpt : The decomposition method provides an effective procedure for analytical solution of a wide and general class of dynamic...
The rheological equation includes the generalized Hooke`s law and Boltzmann`s superposition principle to account for anelasticity. The attenuation properties in different directions, associated with the principal axes of the medium, are controlled by four relaxation functions of viscoelastic type. A ...
Theoretical or Mathematical/ dispersion (wave) integration Korteweg-de Vries equation water waves wave equations/ rational solution general fifth-order shallow water-wave model fifth-order Korteweg-de Vries-like equation KdV-like equation travelling wave solutions long-wavelength limit integration truncated ...