当前位置:文档之家› Handbook of Nonlinear Partial Differential Equationsreferences

Handbook of Nonlinear Partial Differential Equationsreferences

REFERENCES

Ablowitz,M.J.and Segur,H.,Solitons and the Inverse Scattering Transform,Society for Industrial and Applied Mathematics(SIAM),Philadelphia,1981.

Ablowitz,M.J.and Clarkson,P.A.,Solitons,Non-linear Evolution Equations and Inverse Scattering,Cambridge Univ.Press,Cambridge,1991.

Ablowitz,M.J.,Kaup,D.J.,Newell,A.C.,and Segur,H.,The inverse scattering transform—Fourier analysis for nonlinear problems,Stud.Appl.Math.,V ol.53,pp.249–315,1974.

Abramenko,A.A.,Lagno,V.I.,and Samoilenko,A.M.,Group classi?cation of nonlinear evolutionary equations.I.Invariance under semisimple groups of local transformations

[in Russian],Diff.Uravneniya,V ol.38,No.3,pp.365–372,2002.

Abramenko,A.A.,Lagno,V.I.,and Samoilenko,A.M.,Group classi?cation of nonlinear evo-lutionary equations.II.Invariance under solvable groups of local transformations[in Russian],

Diff.Uravneniya,V ol.38,No.4,pp.482–489,2002.

Abramowitz,M.and Stegun,I.A.Handbook of Mathematical Functions with Formulas,Graphs and Mathematical Tables,National Bureau of Standards Applied Mathematics,Washington,

1964.

Ablowitz,M.J.and Zeppetella,A.,Explicit solutions of Fisher’s equation for a special wave speed, Bull.Math.Biology,V ol.41,pp.835–840,1979.

Adler,V.,Shabat,A.V.,and Yamilov,R.I.,Symmetry approach to the integrability problems, Theor.&Math.Phys.,V ol.125,No.3,pp.1603–1661,2000.

Akhatov,I.Sh.,Gazizov,R.K.,and Ibragimov,N.H.,Nonlocal symmetries.Heuristic approach [in Russian],In:Itogi Nauki i Tekhniki,Ser.Sovremennye Problemy Matematiki,Noveishie

Dostizheniya,V ol.34,VINITI,Moscow,1989(English translation in J.Soviet Math.,V ol.55(1),

p.1401,1991).

Akhmediev,N.N.and Ankiewicz,A.,Solitons.Nonlinear Pulses and Beams,Chapman&Hall, London,1997.

Ames,W.F.,Nonlinear Partial Differential Equations in Engineering,Vol.1,Academic Press,New York,1967.

Ames,W.F.,Nonlinear Partial Differential Equations in Engineering,Vol.2,Academic Press,New York,1972.

Ames,W.F.,Lohner,J.R.,and Adams E.,Group properties of u tt=[f(u)u x]x,Int.J.Nonlinear Mech.,V ol.16,No.5–6,p.439,1981.

Anderson,R.L.and Ibragimov,N.H.,Lie–B¨a cklund Transformations in Applications,Society for Industrial and Applied Mathematics(SIAM),Philadelphia,1979.

Andreev,V.K.,Kaptsov,O.V.,Pukhnachov,V.V.,and Rodionov,A.A.,Applications of Group-Theoretical Methods in Hydrodynamics,Kluwer,Dordrecht,1999.

Arrigo,D.,Broadbridge,P.,and Hill,J.M.,Nonclassical symmetry solutions and the methods of Bluman–Cole and Clarkson–Kruskal,J.Math.Phys.,V ol.34,pp.4692–4703,1993.

Aristov,S.N.,Exact periodic and localized solutions of the equation h t=?ln h,J.Appl.Mech.& Tech.Phys.,V ol.40,No.1,pp.16–19,1999.

Aristov,S.N.and Gitman,I.M.,Viscous?ow between two moving parallel disks:exact solutions and stability analysis,J.Fluid Mech.,V ol.464,pp.209–215,2002.

Asta?ev,V.I.,Radayev,Yu.N.,and Stepanova,L.V.,Nonlinear Fracture Mechanics[in Russian], Samarsky University Publ.,Samara,2001.

Baikov,V.A.,Approximate group analysis of nonlinear models of continuum mechanics,Ph.D.

thesis[in Russian],Keldysh Institute of Applied Mathematics,Moscow,1990.

? 2004 by Chapman & Hall/CRC

λθxθy, Theor.&Math.Phys.,V ol.122,No.1,pp.35–45,2000.

Gardner,C.S.,Greene,J.M.,Kruskal,M.D.,and Miura,R.M.,Method for solving the Korteweg–de Vries equation,Phys.Rev.Lett.,V ol.19,No.19,pp.1095–1097,1967.

Gardner,C.S.,Greene,J.M.,Kruskal,M.D.,and Miura,R.M.,Korteweg–de Vries equation and generalizations.VI:Methods for exact solution,Comm.Pure Appl.Math.,V ol.27,p.97–133,

1974.

Gelfand,I.M.,Some problems of the theory of quasi-linear equations,Uspekhi Matem.Nauk, V ol.14,No.2,pp.87–158,1959[Amer.Math.Soc.Translation Series2,pp.295–381,1963].

Gesztesy,F.and Weikard,R.,Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies–an analytic approach,Bull.AMS,V ol.35,No.4,pp.271–317,1998.

Glassey,R.T.,Hunter,J.K.,and Zheng,Y.,Singularities and oscillations in a nonlinear variational wave equation,In:Singularities and Oscillations(Editors J.Ranch and M.Taylor),Springer-

Verlag,New York,1997.

Godlewski,E.and Raviart,P.-A.,Numerical Approximations of Hyperbolic Systems of Conserva-tion Laws,Springer-Verlag,New York,1996.

Golubev,V.V.,Lectures on Analytic Theory of Differential Equations[in Russian],GITTL,Moscow, 1950.

Gorodtsov,V.A.,Heat transfer and turbulent diffusion in one-dimensional hydrodynamics without pressure,Appl.Math.and Mech.(PMM),V ol.62,No.6,pp.1021–1028,1998.

Gorodtsov,V.A.,The effect of a local increase in impurity concentration in one-dimensional hydrodynamics,Appl.Math.and Mech.(PMM),V ol.64,No.4,pp.593–600,2000.

Goursat,E.,A Course of Mathematical Analysis.Vol3.Part1[Russian translation],Gostekhizdat, Moscow,1933.

Grauel,A.,Sinh-Gordon equation,Painlev′e property and B¨a cklund transformation,Physica A, V ol.132,pp.557–568,1985.

Grauel,A.and Steeb,W.-H.,Similarity solutions of the Euler equations and the Navier–Stokes equations in two space dimensions,Int.J.Theor.Phys.,,V ol.24,pp.255–265,1985.

Gromak,V.I.,Painlev′e Differential Equations in the Complex Plane,Walter de Gruyter,Berlin, 2002.

Gromak,V.I.and Lukashevich,N.A.,Analytical Properties of Solutions of Painlev′e Equations [in Russian],Universitetskoe,Minsk,1990.

Grundland,A.M.and Infeld,E.,A family of non-linear Klein-Gordon equations and their solutions,J.Math.Phys.,V ol.33,pp.2498–2503,1992.

Gupalo,Yu.P.,Polyanin,A.D.,and Ryazantsev,Yu.S.,Mass and Heat Transfer of Reacting Particles with the Flow[in Russian],Nauka,Moscow,1985.

Hamdi,S.,Enright,W.H.,Schiesser,W.E.,and Gottlieb,J.J.,Exact solutions of the generalized equal width wave equation,Math.&Comp.in Simulation,2003(to appear).

Hanyga,A.,Mathematical Theory of Nonlinear Elasticity,PWN,Warszawa,1985.

Happel,J.and Brenner,H.,Low Reynolds Number Hydrodynamics,Prentice-Hall,Englewood Cliffs,1965.

Harris,S.E.,Conservation laws for a nonlinear wave equation,Nonlinearity,V ol.9,pp.187–208, 1996.

Hereman,W.,Review of symbolic software for the computation of Lie symmetries of differential equations,Euromath Bull.,V ol.1,pp.45–82,1994.

Hill,J.M.,Solution of Differential Equations by Means of One-Parameter Groups,Pitman, Marsh?eld,Mass.,1982.

? 2004 by Chapman & Hall/CRC

相关主题
文本预览
相关文档 最新文档