期刊
ANNALES HENRI POINCARE
卷 23, 期 7, 页码 2611-2655出版社
SPRINGER INT PUBL AG
DOI: 10.1007/s00023-021-01143-z
关键词
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资金
- National Natural Science Foundation of China [11975306]
- Natural Science Foundation of Jiangsu Province [BK20181351]
- Six Talent Peaks Project in Jiangsu Province [JY-059]
- Fundamental Research Fund for the Central Universities [2019ZDPY07, 2019QNA35]
In this study, we employ the partial derivative-steepest descent method to investigate the Cauchy problem of the WKI equation with initial conditions in weighted Sobolev space H(R). The long time asymptotic behavior of the solution is derived, and based on this behavior, we prove the soliton resolution conjecture of the WKI equation.
In this work, we employ the partial derivative-steepest descent method to investigate the Cauchy problem of the Wadati-Konno-Ichikawa (WKI) equation with initial conditions in weighted Sobolev space H(R). The long time asymptotic behavior of the solution q(x, t) is derived in a fixed spacetime cone S(y(1),y(2),v(1),v(2)) = {(y, t) is an element of R-2 : y = y(0) + vt, y(0) is an element of [y(1),y(2)], v is an element of [v(1), v(2)]}. Based on the resulting asymptotic behavior, we prove the soliton resolution conjecture of the WKI equation which includes the soliton term confirmed by N(I)-soliton on discrete spectrum and the t(-1/2) order term on continuous spectrum with residual error up to O(t(-3/4)).
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