Classical themes concerning the general solutions of the wave equations in the time domain are briefly summarized in this chapter. The solution of a one-dimensional wave equation or plane waves may be formulated from point of view of the linear system theory using the convolution of the impulse ...
Where the potential is zero inside the box, the Schrödinger wave equation becomes where . The general solution is . Quantization Boundary conditions of the potential dictate that the wave function must be zero at x = 0 and x = L. This yields valid solutions for integer values of n such...
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 ...
And therefore the wave equation (1) transforms into u ξη = 0. It is easy to find the general solution to this equation by integration twice. First suppose you integrate with respect to η and notice that the constant of integration depends on ξ to get u ξ = C(ξ). Now integrat...
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...
Feasible fundamental solution of the multiphysics wave equation in inhomogeneous domains of complex shape 喜欢 0 阅读量: 16 作者:Ayzenberg,Alena,A.,Aizenberg,Arkady,M.摘要: Fundamental solutions of the linear equations gove 年份: 2015 收藏 引用 批量引用 报错 分享 ...
Rigorous results are obtained that establish the existence and stability of traveling-wave solitary-wave solutions to the nonlocal Benjamin-Ono equation, η t +2ηη x -lη xx -η xxx =0, where η(x,t) is a real-valued function, l is a constant, and is a symbol standing for the ...
(x_1,x_2,y_1,y_2,t_1,t_2\). This fact is not surprising. Indeed, in general if an equation involves a complex parameter, the solution depends on both the real and the imaginary parts of this parameter. For example, the time-independent part of the Lax pair Eq. (2.1) or ...
4. Conclusions In this Letter, making use of a new more general ansatze, the extended tanh-function method is generalized, called generalized extended tanh-function method, for finding the exact solutions of NPDEs, and applied to WZ equation. As a result, seventeen families of soliton solutions...
Here, we analyze the impact of different spatial grids, based on the crystallography cubic system, over the accuracy of the solution as well as its computational cost; keeping in mind not only the solution of the wave equation but also a forward look at Maxwell’s equations. Fig. 1 shows ...