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2011•Chinese Physics BRequires access

Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order

Qinghua Feng, Fanwei Meng, Yaoming Zhang

Open publisher page 4 citations

Abstract

In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin—Bona—Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method.

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What this paper is about

In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin—Bona—Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method.

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OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin—Bona—Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method.

Key concepts: Ode, Riccati equation, Nonlinear system, Ordinary differential equation, Traveling wave, Algebraic Riccati equation, Applied mathematics, Order (exchange)

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