Traveling Wave Solutions to the Davey-Stewartson Equation With the Riccati-Bernoulli Sub-ODE Method

YANG Xiao-feng; DENG Zi-chen; WEI Yi

doi:10.3879/j.issn.1000-0887.2015.10.006

Volume 36 Issue 10

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YANG Xiao-feng, DENG Zi-chen, WEI Yi. Traveling Wave Solutions to the Davey-Stewartson Equation With the Riccati-Bernoulli Sub-ODE Method[J]. Applied Mathematics and Mechanics, 2015, 36(10): 1067-1075. doi: 10.3879/j.issn.1000-0887.2015.10.006

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Traveling Wave Solutions to the Davey-Stewartson Equation With the Riccati-Bernoulli Sub-ODE Method

doi: 10.3879/j.issn.1000-0887.2015.10.006

¹Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, P.R.China;²Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an 710072, P.R.China

Received Date: 2015-06-24
Rev Recd Date: 2015-07-23
Publish Date: 2015-10-15

Abstract

Abstract

The Riccati-Bernoulli subsidiary ordinary differential equation (sub-ODE) method was proposed to construct the exact traveling wave solutions to the nonlinear partial differential equations (NLPDEs). Through traveling wave transformation, the NLPDE was reduced to a nonlinear ODE. With the aid of the Riccati-Bernoulli sub-ODE, the nonlinear ODE was converted into a set of nonlinear algebraic equations. The exact traveling wave solutions to the NLPDE were obtained as soon as this set of nonlinear algebraic equations were solved. Application of this method to the Davey-Stewartson equation directly gave the exact traveling wave solutions. The Bcklund transformation of the Davey-Stewartson equation was also given. The results were compared with those of the first-integral method. The proposed method is effective and easy to be generalized to deal with other types of nonlinear partial differential equations.
- Riccati-Bernoulli sub-ODE method,
- Davey-Stewartson equation,
- traveling wave solution,
- Backlund transformation

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References

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