An extended subequation rational expansion method with symbolic computation and solutions of the nonlinear Schrödinger equation model

2008 ◽  
Vol 2 (2) ◽  
pp. 242-255 ◽  
Author(s):  
Yong Chen ◽  
Biao Li
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Symbolic Computation ◽  
Schrodinger Equation ◽  
Expansion Method ◽  
Equation Model ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger

NEW ENVELOPE SOLUTIONS FOR COMPLEX NONLINEAR SCHRÖDINGER+ EQUATION VIA SYMBOLIC COMPUTATION

2003 ◽  
Vol 14 (02) ◽  
pp. 225-235 ◽  
Author(s):  
ZHEN-YA YAN
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Symbolic Computation ◽  
Schrodinger Equation ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Nonlinear Schrodinger Equation ◽  
Jacobian Elliptic Functions ◽  
Nonlinear Schrödinger ◽  
Trigonometric Function Solutions

With the aid of symbolic computation, an extended Jacobian elliptic function expansion method is further extended to the complex nonlinear Schrödinger + equation. As a result, 24 families of the envelope doubly-periodic solutions with Jacobian elliptic functions are obtained. When the modulus m → 1 or zero, the corresponding six envelope solitary wave solutions and six envelope singly-periodic (trigonometric function) solutions are also found. This powerful method can also be applied to other equations, such as the nonlinear Schrödinger equation and Zakharov equation.

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