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醉染图书非线波数学物理学入门9787560396163
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1 Nonlinearity in classical mechanics1.1 A pendulum1.1.1 Oscillation1.1.2 Vertical rotation1.2 Vibration by a nonlinear spring force1.3 A jumping rope1.4 Hyperbolic and elliptic functions1.4.1 Definitions1.4.2 Differentiation1.4.3 Reverse functions cn-1 and dn-11.4.4 Periodicity of Jacobis sn-function1.5 Variation principle1.6 Buckling deformation of a rodExercise2 Wave propagation,singularities and boundaries2.1 Elastic waves along a linear string of infinite lent2.1.1 Phase of propagation2.1.2 Energy flow2.1.3 Scattering by an oscillator2.2 Microwave transmission. Schr6dingers equation2.4 Scattering by the potential V(x)=Vo sech2 x2.5 Two-dimensional waves in inhomogeneous medium2.6 Sound propagation in airExercises3 Solitons and adiabatic potentials3.t The Korteweg-deVries equation3.2 Steady solutions of the Korteweg-deVries equation3.3 Developing equations of nonlinear vector waves3.4 Bargmanns theorem3.4.1 One-soliton solution3.4.2 Two-soliton solution3.5 Riccatis theorem3.6 Properties of the Eckart potential in the soliton field3.7 Zabusky-Kruskals computational analysisExercises4 Structural phase transitions4.1 Initial uncertainties and transition anomalies4.1.1 Specific heat anomalies4.1.2 Landaus theory4.2 Dynamical theory of collective motion4.2.1 Longitudinal waves4.2.2 Transverse waves4.3 Pseudopotential and sine-Gordon equationExercises5 Nonlinear waves5.1 Elemental waves5.2 Matrix formulation for nonlinear development5.3 Heat dissipation of wave motion5.4 Born-Huang transitions in crystals5.5 Symmetry of media for the Korteweg-deVries equation5.6 Soliton descriptionExercise6 Scattering theory6.1 One-component waves6.1.1 Scatterings of elemental waves6.1.2 Singularity of a soliton potential6.2 Two-component scatterings6.2.1 A two-component wave6.2.2 Reflection and transmission6.. Poles of transmission and reflection coefficients6.2.4 Soliton potentials6.2.5 Asymptotic expansionExercises7 Method of inverse scatterings7.1 Coherent wave packets and Marchenkos equation7.1.1 Delta and truncated step functions for coherent wave packets7.1.2 Fourier transforms and Marchenkos equations7.2 Reflectionless multi-soliton potentials7.3 Two-component systems7.3.1 Inverse scatterings7.3.2 Matrix method7.3.3 Modified Korteweg-deVries equation,part 1Exercises8 si-static soliton states8.1 Developing the Korteweg-deVries equation8.1.1 N onstationary states8.1.2 Thermal perturbation8.2 Multi-soliton potentials in unsteady states8.3 The modified Korteweg-deVries equation,part 28.4 Thermodynamic instability and Breezer potentials8.5 The third-order Schrodinger equationExercises9 The Baicklund transformation and sine-Gordon equations9.1 The Klein-Gordon equation9.2 The Backlund transformation9.3 The sine-Gordon equation9.4 Numerical analysis of the sine-Gordon equation9.5 Inverse scatterings and the Backlund transformation9.6 Scatterings by a pseudopotential10 Miscellaneous applications10.1 Surface waves10.1.1 The first approximation10.1.2 The second approximation10.2 Vortex motion in fluid media10.2.1 A vortex10.2.2 Vortex motion10.3 Plasma oscillation10.4 Laser light transmission throu asorbing media10.4.1 Two-level atom in an intense radiation field10.4.2 Scattering of intense radiation10.4.3 Sine-Gordon limit10.5 Periodic lattices10.5.1 Tos ttce10.5.2 Aperiodic transitions by pseudopotentials编辑手记
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