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Soliton Resolution for the Wadati-Konno-Ichikawa Equation with Weighted Sobolev Initial Data

机译:Soliton Resolution for the Wadati-Konno-Ichikawa Equation with Weighted Sobolev Initial Data

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摘要

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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