This paper applies function transformation method to obtain under certain conditions bright, dark, kink and W-shaped dark solitons waves solutions the modified Complex Ginzburg Landau Equation.The relevant aspect that is encountered using applied ability lead many types of interesting soliton model. These new obtained can be useful in applications such as communication, medicine, hydrodynamic, ...

We provide the solutions of Linear Left-invariant 2nd-order Evolution Equations on the 2D-Euclidean motion group. These solutions are given by group convolution with the corresponding Green’s functions which we derive in explicit form. A particular case coincides with the Forward Kolmogorov equation of the direction process, the exact solution of which was strongly required in the field of imag...

We provide the solutions of linear, left-invariant, 2nd-order stochastic evolution equations on the 2D-Euclidean motion group. These solutions are given by group-convolution with the corresponding Green’s functions that we derive in explicit form in Fourier space. A particular case coincides with the hitherto unsolved forward Kolmogorov equation of the so-called direction process, the exact sol...

New fonnulae providing exact explicit solutions for a class of scalar delayed systems are given.

In this paper, the Exp-function method, with the aid of a symbolic computation system such as Maple, is applied to the (2+1) -dimensional Calogero Bogoyavlanskii Schiff equation. Exact and explicit generalized solitary solutions are obtained in more general forms. The free parameters can be determined by initial or boundary conditions. The method is straightforward and concise, and its applicat...

The fractional derivatives in the sense of modified Riemann-Liouville derivative and the improved fractional sub-equation method are employed for constructing the exact solutions of nonlinear fractional partial differential equations. By means of this method, the space-time fractional generalized Hirota-Satsuma coupled Kortewegde Vries equations are successfully solved. As a result, three types...