Symbolic methods to construct exact solutions of nonlinear partial differential equations
Tóm tắt
Từ khóa
Tài liệu tham khảo
Ablowitz, 1991
Ablowitz, 1981
Ablowitz, 1979, Explicit solutions of Fisher's equation for a special wave speed, Bull. Math. Biology, 41, 835, 10.1007/BF02462380
Calogero, 1987, The evolution partial differential equation ut = uxxx + 3(uxxu2 + 3ux2u) + 3uxu4, J. Math. Phys., 28, 538, 10.1063/1.527639
Calogero, 1991, Why are certain nonlinear PDEs both widely applicable and integrable?
Caudrey, 1976, A new hierarchy of Korteweg-de Vries equations, 351, 407
Dodd, 1977, The prolongation structure of a higher order Korteweg-de Vries equation, 358, 287
Drazin, 1989
Fordy, 1980, Some remarkable nonlinear transformation, Phsy. Lett. A, 75, 325, 10.1016/0375-9601(80)90829-4
Hereman, 1993, Symbolic software for the study of nonlinear partial differential equations, VII, 326
Hereman, 1992, Symbolic computation of solitons with Macsyma, 287
Hereman, 1995, Symbolic software for soliton theory, Acta Applicandae Mathematicae, 39, 361, 10.1007/BF00994643
Hirota, 1980, The Miura transformation of Kaup's equation and of Mihailov's equation, Phys. Lett. A, 76, 95, 10.1016/0375-9601(80)90578-2
Ito, 1980, An extension of nonlinear evolution equations of the K-dV (mK-dV) type to higher orders, J. Phys. Soc. Japan, 49, 771, 10.1143/JPSJ.49.771
Jimbo, 1983, Solitons and infinite dimensional Lie algebras, 19, 943
Kaup, 1980, On the inverse scattering problem for the cubic eigenvalue problems of the class ψ3x + 6Qψx + 6Rψ = λψ, Stud. Appl. Math., 62, 189, 10.1002/sapm1980623189
Kawahara, 1983, Interactions of traveling fronts: an exact solution of a nonlinear diffusion equation, Phys. Lett. A, 97, 311, 10.1016/0375-9601(83)90648-5
Kupershmidt, 1984, A super KdV equation: an integrable system, Phys. Lett. A, 102, 213, 10.1016/0375-9601(84)90693-5
Lax, 1968, Integrals of nonlinear equations of evolution and solitary waves, Comm. Pure Appl. Math., 21, 467, 10.1002/cpa.3160210503
Malfliet, 1994
Mafliet, 1994, The tanh method in nonlinear wave theory
Murray, 1989, 19
Nuseir, 1995, Symbolic computation of exact solutions of nonlinear partial differential equations using direct method
Satsuma, 1977, A Bäcklund transformation for a higher order Korteweg-de Vries equation, J. Phys. Soc. Japan, 43, 692, 10.1143/JPSJ.43.692