An integrable generalization of the nonlinear Schr\"odinger equation on the half-line and solitons
作者： A. S. Fokas , J. Lenells
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摘要: We analyze initial-boundary value problems for an integrable generalization of the nonlinear Schrodinger equation formulated on half-line. In particular, we investigate so-called linearizable boundary conditions, which in this case are Robin type. Furthermore, use a particular solution to verify explicitly all steps needed well-posed problem.
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core.ac.uk参考文章(15)
A.S. Fokas, Integrable Nonlinear Evolution Equations on the Half-Line Communications in Mathematical Physics. ,vol. 230, pp. 1- 39 ,(2002) , 10.1007/S00220-002-0681-8
B. Fuchssteiner, A.S. Fokas, Symplectic structures, their Bäcklund transformations and hereditary symmetries Physica D: Nonlinear Phenomena. ,vol. 4, pp. 47- 66 ,(1981) , 10.1016/0167-2789(81)90004-X
A. S. Fokas, A. R. Its, The linearization of the initial-boundary value problem of the nonlinear Schro¨dinger equation Siam Journal on Mathematical Analysis. ,vol. 27, pp. 738- 764 ,(1996) , 10.1137/0527040
Jonatan Lenells, The derivative nonlinear Schrodinger equation on the half-line Physica D: Nonlinear Phenomena. ,vol. 237, pp. 3008- 3019 ,(2008) , 10.1016/J.PHYSD.2008.07.005
A. Boutet de Monvel, A. S. Fokas, D. Shepelsky, Analysis of the Global Relation for the Nonlinear Schrödinger Equation on the Half-line Letters in Mathematical Physics. ,vol. 65, pp. 199- 212 ,(2003) , 10.1023/B:MATH.0000010711.66380.77
A. R. Its, L.-Y. Sung, A. S. Fokas, The nonlinear Schrödinger equation on the half-line Nonlinearity. ,vol. 18, pp. 1771- 1822 ,(2005) , 10.1088/0951-7715/18/4/019
A. S. Fokas, A unified transform method for solving linear and certain nonlinear PDEs Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences. ,vol. 453, pp. 1411- 1443 ,(1997) , 10.1098/RSPA.1997.0077
V. E. Zakharov, A. B. Shabat, A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I Functional Analysis and Its Applications. ,vol. 8, pp. 226- 235 ,(1975) , 10.1007/BF01075696
Roberto Camassa, Darryl D. Holm, An integrable shallow water equation with peaked solitons Physical Review Letters. ,vol. 71, pp. 1661- 1664 ,(1993) , 10.1103/PHYSREVLETT.71.1661
A.S. Fokas, A.R. Its, An initial-boundary value problem for the Korteweg-de Vries equation Mathematics and Computers in Simulation. ,vol. 37, pp. 293- 321 ,(1994) , 10.1016/0378-4754(94)00021-2