In this paper, the tanh and sine–cosine methods are used to construct exact periodic and soliton solutions of nonlinear evolution equations arising in mathematical physics. Many new families of exact travelling wave solutions of the generalized Hirota–Satsuma coupled KdV system, generalized-Zakharov equations and (2 + 1)-dimensional Broer–Kaup– Kupershmidt system are successfully obtained. The ...

to start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ode. then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. it is required to state that the infinite series method is a well-organized method for obtaining exact s...

It is well known that fractional differential equations appeared more and more frequently in different research areas, such as fluid mechanics, viscoelasticity, biology, physics, engineering and other areas of science [1-30]. Considerable attention have been spent in recent years to develop techniques to look for solutions of nonlinear fractional partial differential equations (NFPDEs). Consequ...

In the paper, with the aid of symbolic computation, we investigate the generalized Hirota–Satsuma coupled KdV system via our Weierstrass semi-rational expansion method presented recently using the rational expansion of Weierstrass elliptic function and its first-order derivative. As a consequence, three families of newWeierstrass elliptic function solutions via Weierstrass elliptic function }(n...

In this paper a new Weierstrass semi-rational expansion method is developed via the Weierstrass elliptic function ℘(ξ; g2, g3). With the aid of Maple, we choose the coupled water wave equation and the generalized Hirota-Satsuma coupled KdV equation to illustrate the method. As a consequence, it is shown that the method is powerful to obtain many types of new doubly periodic solutions in terms o...