A new technique for constructing conservation laws for fractional differential equations not
having a Lagrangian is proposed. The technique is based on the methods of Lie group …

Some of the most important geometric integrators for both ordinary and partial differential
equations are reviewed and illustrated with examples in mechanics. The class of …

In this paper, we analyze the dynamic behavior of the ill-posed Boussinesq equation (IPBE)
that arises in nonlinear lattices and also in shallow water waves. Some solitary wave …

In this manuscript, we utilized the algorithm of Riccati–Bernoulli sub-ODE method to find
new soliton solutions to the Kudryashov–Sinelshchikov equation (KSE). Some new type of …

In this work, we investigate the soliton solutions to the resonant nonlinear Shrödinger's
equation (R-NSE) with Kerr law nonlinearity. By adopting the Riccati–Bernoulli sub-ODE …

The resonant nonlinear Shrödinger's equation (RNLSE) with both spatio-temporal (STD)
and inter-modal (IMD) dispersions which describes the modelling of fluids and propagation …

This paper studies the dynamics of solitons to the nonlinear Schrödinger's equation (NLSE)
with spatio-temporal dispersion (STD). The integration algorithm that is employed in this …

In this work, the Riccati-Bernoulli sub-ordinary differential equation and modified tanh-coth
methods are used to reach soliton solutions of the nonlinear evolution equation. We acquire …

In this paper, the Riccati-Bernoulli sub-ODE method is used to find the soliton solutions of
two different fifth-order nonlinear partial differential equations (NPDEs). The efficiency of this …

In this paper we study the generalized variable-coefficient Gardner equations of the form u t+
A (t) unu x+ C (t) u 2 nu x+ B (t) uxx x+ Q (t) u= 0. This class broadens out many other …