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New Exact Travelling Wave Solutions for Generalized Zakharov-Kuzentsov EquationsUsing General Projective Riccati Equation Method 被引量:14
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作者 CHENYong LIBiao 《Communications in Theoretical Physics》 SCIE CAS CSCD 2004年第1期1-6,共6页
Applying the generalized method, which is a direct and unified algebraic method for constructing multipletravelling wave solutions of nonlinear partial differential equations (PDEs), and implementing in a computer alg... Applying the generalized method, which is a direct and unified algebraic method for constructing multipletravelling wave solutions of nonlinear partial differential equations (PDEs), and implementing in a computer algebraicsystem, we consider the generalized Zakharov-Kuzentsov equation with nonlinear terms of any order. As a result, wecan not only successfully recover the previously known travelling wave solutions found by existing various tanh methodsand other sophisticated methods, but also obtain some new formal solutions. The solutions obtained include kink-shapedsolitons, bell-shaped solitons, singular solitons, and periodic solutions. 展开更多
关键词 projective riccati equation method generalized Zakharov-Kuzentsov equation exact solutions
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Application of Extended Projective Riccati Equation Method to(2+1)-Dimensional Broer-Kaup-Kupershmidt System 被引量:1
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作者 LU Bin ZHANG Hong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第10期814-820,共7页
In this paper, extended projective Riccati equation method is presented for constructing more new exact solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than pro... In this paper, extended projective Riccati equation method is presented for constructing more new exact solutions of nonlinear differential equations in mathematical physics, which is direct and more powerful than projective Riccati equation method. In order to illustrate the effect of the method, Broer Kaup Kupershmidt system is employed and Jacobi doubly periodic solutions are obtained. This algorithm can also be applied to other nonlinear differential equations. 展开更多
关键词 nonlinear- partial differential equations extended projective riccati equation method exact solutions Broer- Kaup Kupershmidt system
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Exact Solutions to Extended Nonlinear Schrodinger Equation in Monomode Optical Fiber 被引量:1
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作者 BAI Cheng-Lin ZHAO Hong Wang Wei-Tao 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第1期131-134,共4页
By using the generally projective Riccati equation method, more new exact travelling wave solutions to extended nonlinear Schrodinger equation (NLSE), which describes the femtosecond pulse propagation in monomode op... By using the generally projective Riccati equation method, more new exact travelling wave solutions to extended nonlinear Schrodinger equation (NLSE), which describes the femtosecond pulse propagation in monomode optical fiber, are found, which include bright soliton solution, dark soliton solution, new solitary waves, periodic solutions, and rational solutions. The finding of abundant solution structures for extended NLSE helps to study the movement rule of femtosecond pulse propagation in monomode optical fiber. 展开更多
关键词 extended NLSE generally projective riccati equation method soliton solutions optical fiber
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New Exact Travelling Wave Solutions to Hirota Equation and (1+1)-Dimensional Dispersive Long Wave Equation
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作者 WANGQi CHENYong +1 位作者 LIBiao ZHANGHong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2004年第6期821-828,共8页
Based on the computerized symbolic Maple, we study two important nonlinear evolution equations, i.e., the Hirota equation and the (1+1)-dimensional dispersive long wave equation by use of a direct and unified algebrai... Based on the computerized symbolic Maple, we study two important nonlinear evolution equations, i.e., the Hirota equation and the (1+1)-dimensional dispersive long wave equation by use of a direct and unified algebraic method named the general projective Riccati equation method to find more exact solutions to nonlinear differential equations. The method is more powerful than most of the existing tanh method. New and more general form solutions are obtained. The properties of the new formal solitary wave solutions are shown by some figures. 展开更多
关键词 projective riccati equation method (1+1)-dimensional dispersive long wave equation Hirota equation
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