Long-time asymptotics for the Fokas-Lenells equation with decaying initial value problem: Without solitons

Abstract We use the Deift–Zhou method to obtain, in the solitonless sector, the leading order asymptotic of the solution to the Cauchy problem of the Fokas–Lenells equation as t → + ∞ on the full-line.

[1]  J. Lenells.  Exactly Solvable Model for Nonlinear Pulse Propagation in Optical Fibers , 2008, 0810.5289.

[2]  A. Vartanian,et al.  Asymptotics of Solutions to the Modified Nonlinear Schr , 1997, solv-int/9801001.

[3]  F. As,et al.  Soliton generation for initial-boundary-value problems. , 1992 .

[4]  J. Timonen,et al.  Optical soliton in the presence of perturbations , 1993 .

[5]  A. S. Fokas,et al.  On a novel integrable generalization of the nonlinear Schrödinger equation , 2008, 0812.1510.

[6]  Athanassios S. Fokas,et al.  On a novel integrable generalization of the sine-Gordon equation , 2010 .

[7]  A. Fokas.  On a class of physically important integrable equations , 1994 .

[8]  A. Vartanian.  Higher order asymptotics of the modified non-linear schrödinger equation , 1998, solv-int/9804013.

[9]  Ronald R. Coifman,et al.  Scattering and inverse scattering for first order systems , 1984 .

[10]  P. Deift,et al.  A steepest descent method for oscillatory Riemann–Hilbert problems. Asymptotics for the MKdV equation , 1992, math/9201261.

[11]  Yoshimasa Matsuno,et al.  A direct method of solution for the Fokas–Lenells derivative nonlinear Schrödinger equation: I. Bright soliton solutions , 2012, 1205.3243.

[12]  A. S. Fokas,et al.  An integrable generalization of the nonlinear Schrödinger equation on the half-line and solitons , 2008, 0812.1335.

[13]  V. Zakharov,et al.  Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II , 1979 .

[14]  Leading-order temporal asymptotics of the modified nonlinear Schrödinger equation: solitonless sector , 1996, solv-int/9701001.

[15]  V. E. Vekslerchik,et al.  Lattice representation and dark solitons of the Fokas–Lenells equation , 2011, 1103.4701.

[16]  P. Schuur.  Asymptotic analysis of soliton problems , 1986 .

[17]  G. Teschl,et al.  Long-Time Asymptotics for the Korteweg–de Vries Equation via Nonlinear Steepest Descent , 2008, 0807.5041.

[18]  P. Deift,et al.  A steepest descent method for oscillatory Riemann–Hilbert problems. Asymptotics for the MKdV equation , 1993 .

[19]  Gerald Teschl,et al.  Long-time Asymptotics for the Camassa-Holm Equation , 2009, SIAM J. Math. Anal..

[20]  Jonatan Lenells,et al.  Dressing for a Novel Integrable Generalization of the Nonlinear Schrödinger Equation , 2009, J. Nonlinear Sci..

[21]  S. Venakides,et al.  LONG-TIME ASYMPTOTICS FOR THE PURE RADIATION SOLUTION OF THE SINE-GORDON EQUATION , 1999 .

[22]  Percy Deift,et al.  Long-Time Asymptotics for Integrable Nonlinear Wave Equations , 1993 .