CAUCHY PROBLEM FOR THE GENERALIZED DAVEY-STEWARTSON SYSTEMS IN BESOV SPACES AND SOME COUNTEREXAMPLES

Wenjing Song; Ganshan Yang

doi:10.11948/20190257

2020 Volume 10 Issue 6

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Wenjing Song, Ganshan Yang. CAUCHY PROBLEM FOR THE GENERALIZED DAVEY-STEWARTSON SYSTEMS IN BESOV SPACES AND SOME COUNTEREXAMPLES[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2418-2438. doi: 10.11948/20190257

Citation:

Wenjing Song, Ganshan Yang. CAUCHY PROBLEM FOR THE GENERALIZED DAVEY-STEWARTSON SYSTEMS IN BESOV SPACES AND SOME COUNTEREXAMPLES[J]. Journal of Applied Analysis & Computation, 2020, 10(6): 2418-2438. doi: 10.11948/20190257

CAUCHY PROBLEM FOR THE GENERALIZED DAVEY-STEWARTSON SYSTEMS IN BESOV SPACES AND SOME COUNTEREXAMPLES

Wenjing Song¹,
Ganshan Yang^2, ,

1.
School of Science, Xi'an Polytechnic University, Xi'an 710048, China
2.
Department of mathematics, Yunnan Nationalities University, Kunming P. O. 650031, China

Corresponding author: Email address:ganshanyang@aliyun.com(G. Yang)

Abstract

Abstract

In this paper, the Cauchy problem of the generalized ellipse-ellipse type Davey-Stewartson systems is discussed. When the dimension of space is greater than or equal to two, we get a unique global solution in Besov spaces by contraction mapping argument. Moreover, by using the F-expansion method, the exact periodic wave solutions for the generalized ellipse-ellipse type DaveyStewartson systems are discussed, some counter examples are given.
- Davey-Stewartson systems /
- F-expansion method /
- multi-order exact solutions /
- Lam function /
- Cauchy problem
MSC: 31A30

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References

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