The homogeneous balance method can be used to construct exact traveling wave solutions of nonlinear partial differential equations. In this paper, this method is used to construct new soliton solutions of the (3+1) Jimbo--Miwa equation.

The wave equation occurs in many branches of physics, in applied mathematics as well as in engineering, and it is also considered as one of the three fundamental equations in mathematical physics. The homogenous wave equation with constant coefficient can be solved by many ways such as separation of variables [1], the methods of characteristics [2, 3], and Laplace transform and Fourier transfor...

We recover the amplitudes of the reflectivity function obtained by wave-equation migration by compensating for the amplitude distortions created by the imaging condition and by the incomplete reflector illumination. The amplitude effects produced by the imaging condition must be taken into account even for simple velocity models, and they are perfectly compensated by a diagonal scaling in the f...

This work aims at introducing some energy operators linked to the Teager-Kaiser energy operator and expands it from time to space in the real domain. We then show the decomposition of the functions of space and time differentiable at least twice in R using those energy operators. The second part of the work focuses on using the energy operators to redefine the general wave equation. The method ...