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Sirendaoreji

Publications and source records attributed to Sirendaoreji.

4 recordsLinked to original sources
arXiv2022

Weierstrass type projective Riccati equation expansion method and solutions of KdV equation

This paper presents two new Weierstrass elliptic function solutions of the projective Riccati equations and four conversion formulas for converting the Weierstrass elliptic functions to the hyperbolic and trigonometric functions. The Weierstrass elliptic function solutions to the projective Riccati equations and the conversion formulas are used to propose the called Weierstrass type projective Riccati equation expansion method. The Weierstrass elliptic function solutions, the solitary wave and the periodic wave solutions of the KdV equation are constructed by using the proposed method. The solitary wave like and the periodic wave solutions of the KdV equation are shown through some figures.

nlin.SI↗
arXiv2020

Exponential--Weierstrass type, exponential--Jacobi type and solitary type solutions to some conformable fractional equations

A new algebraic method to find two special types of exact traveling wave solutions and the solitary type solutions to some conformable fractional partial differential equations is proposed. The two special types of solutions given by the product of exponential and Weierstrass elliptic functions, and the product of exponential and Jacobi elliptic functions are new and they cannot be obtained by using the existing algebraic methods.

math.CA↗
arXiv2018

On classification of the solutions for general elliptic equation

The Bäcklund transformations and the superposition formulas for two sub--equations of the general elliptic equation are constructed from the Riccati equation by using an indirect mapping method.The thirty-six previously known solutions of the general elliptic equation are proved to be equivalent to the another ten solutions.The classification of solutions for the general elliptic equation is obtained based on the equivalence relations.The general elliptic equation expansion method with new classified solutions are used to obtain abundant new exact traveling wave solutions of a modified Camassa-Holm equation.

nlin.SI↗