From breather solutions to lump solutions:A construction method for the Zakharov equation  

作　　者：袁丰 Behzad Ghanbari 张永帅 Abdul Majid Wazwaz Feng Yuan;Behzad Ghanbari;Yongshuai Zhang;Abdul Majid Wazwaz(College of Science,Nanjing University of Posts and Telecommunications,Nanjing 210023,China;Department of Mathematics,Kermanshah University of Technology,Kermanshah,Iran;Department of Mathematics,Shaoxing University,Shaoxing 312000,China;Department of Mathematics,Saint Xavier University,Chicago,IL 60655,USA)

机构地区：[1]College of Science,Nanjing University of Posts and Telecommunications,Nanjing 210023,China [2]Department of Mathematics,Kermanshah University of Technology,Kermanshah,Iran [3]Department of Mathematics,Shaoxing University,Shaoxing 312000,China [4]Department of Mathematics,Saint Xavier University,Chicago,IL 60655,USA

出　　处：《Chinese Physics B》2023年第12期162-169,共8页中国物理B（英文版）

基　　金：sponsored by NUPTSF (Grant Nos.NY220161 and NY222169);the Foundation of Jiangsu Provincial Double-Innovation Doctor Program (Grant No.JSSCBS20210541);the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (Grant No.22KJB110004);the National Natural Science Foundation of China (Grant No.12171433)。

摘　　要：Periodic solutions of the Zakharov equation are investigated.By performing the limit operationλ_(2l-1)→λ_(1)on the eigenvalues of the Lax pair obtained from the n-fold Darboux transformation,an order-n breather-positon solution is first obtained from a plane wave seed.It is then proven that an order-n lump solution can be further constructed by taking the limitλ_(1)→λ_(0)on the breather-positon solution,because the unique eigenvalueλ_(0)associated with the Lax pair eigenfunctionΨ(λ_(0))=0 corresponds to the limit of the infinite-periodic solutions.A convenient procedure of generating higher-order lump solutions of the Zakharov equation is also investigated based on the idea of the degeneration of double eigenvalues in multi-breather solutions.

关 键 词：Zakharov equation breather solution b-positon solution lump solution 

分 类 号：O175[理学—数学]