In this paper, a new construction of exact solutions based on the improved generalized Riccati equation mapping method with modified Reimann-Luiviile fractional derivative and symbolic computation is proposed for seeking abundant solutions of the space-time fractional fifth-order nonlinear Sawada-Kotera equation. The proposed method is very simple, direct, effective and convenient for obtaining...

Extending the gauge-invariance principle for τ functions of the standard bilinear formalism to the supersymmetric case, we define N=1 supersymmetric Hirota operators. Using them, we bilinearize SUSY KdV-type equations (KdV, Sawada-Kotera-Ramani, Hirota-Satsuma). The solutions for multiple collisions of super-solitons and extension to SUSY sine-Gordon are also discussed.

We consider the solution of spectral problems with elliptic potentials in the framework of the Hermite ansatz. We show that the search for potentials and their spectral characteristics is reduced to a system of polynomial equations solvable by the Gröbner bases method and others. New potentials and corresponding solutions of the Sawada–Kotera, Kaup–Kupershmidt, Boussinesq equations are found.

K e y w o r d s N a v i e r S t o k e s equations, Stokes equations, Convergence, Finite element method, Newton's method. 1. I N T R O D U C T I O N In the course of so lv ing non l inear equa t ions like Navie r -S tokes equa t ions , one m a y e m p l o y N e w t o n and Newtonl ike m e t h o d s combin ing wi th o the r m e t h o d s (see, for example , [1-3], etc.) . I t is well known t h a...

In this paper, a new (2 + 1)-dimensional nonlinear evolution equation is investigated. This called the Kadomtsev–Petviashvili–Sawada–Kotera–Ramani equation, which can be seen as two-dimensional extension of Korteweg–de Vries–Sawada–Kotera–Ramani equation. By means Hirota’s bilinear operator and binary Bell polynomials, form Bäcklund transformation are obtained. Furthermore, by application Hopf-...

solitary wave solutions to the broer-kaup equations and approximate long water wave equa-tions are considered challenging by using the rst integral method.the exact solutions obtainedduring the present investigation are new. this method can be applied to nonintegrable equa-tions as well as to integrable ones.

This paper presents a brief instructions to nd geodesics equa-tions on two dimensional surfaces in R3. The resulting geodesic equations are solved numerically using Computer Program Matlab, the geodesics are dis-played through Figures.

In this paper, we construct a Darboux transformation and the related Backlund for super-symmetric Sawada-Kotera (SSK) equation. The associated nonlinear superposition formula is ...

We study master equations of the form $(\partial_t+L)^su=f {in}~\mathbb{R}\times\Omega,$ where $L$ is a divergence elliptic operator and $\Omega\subseteq\mathbb{R}^n$. These are nonlocal equa...