The Complex WKB Method for Nonlinear Equations I: Linear Theory by Victor P. MaslovThe Complex WKB Method for Nonlinear Equations I: Linear Theory by Victor P. Maslov

The Complex WKB Method for Nonlinear Equations I: Linear Theory

byVictor P. MaslovEditorM.A. Shishkova, A.B. Sossinsky

Paperback | October 6, 2012

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This book deals with asymptotic solutions of linear and nonlinear equa­ tions which decay as h ---+ 0 outside a neighborhood of certain points, curves and surfaces. Such solutions are almost everywhere well approximated by the functions cp(x) exp{iS(x)/h}, x E 1R3, where S(x) is complex, and ImS(x) <_20_020_and20_develop20_the20_method20_for20_a20_wide20_class20_of20_problems20_in20_mathematical20_physics.20_asymptotics20_of20_this20_type20_were20_constructed20_recently20_for20_many20_linear20_probc2ad_20_lems20_of20_mathematical20_physics3b_20_certain20_specific20_formulas20_were20_obtained20_by20_differc2ad_20_ent20_methods20_28_v.20_m.20_babich20_5b_520_-75d_2c_20_v.20_p.20_lazutkin20_5b_765d_2c_20_a.20_a.20_sokolov2c_20_1.20_m.20_terc2ad_20_nov20_5b_1135d_2c_20_j.20_schwinger20_5b_1072c_20_1085d_2c_20_e.20_j.20_heller20_5b_535d_2c_20_g.20_a.20_hagedorn20_5b_502c_20_515d_2c_20_v.20_n.20_bayer2c_20_v.20_m.20_katkov20_5b_215d_2c_20_n.20_a.20_chernikov20_5b_355d_20_and20_others29_.20_however2c_20_a20_general20_28_hamiltonian29_20_formalism20_for20_obtaining20_asymptotics20_of20_this20_type20_is20_clearly20_required3b_20_this20_state20_of20_affairs20_is20_expressed20_both20_in20_recent20_mathematical20_and20_physical20_literature.20_for20_example2c_20_the20_editors20_of20_the20_collected20_volume20_5b_1065d_20_write20_in20_its20_preface3a_20_22_one20_can20_hope20_that20_in20_the20_near20_future20_a20_computational20_proc2ad_20_cedure20_for20_fields20_with20_complex20_phase2c_20_similar20_to20_the20_usual20_one20_for20_fields20_with20_real20_phase2c_20_will20_be20_developed. 0="" and="" develop="" the="" method="" for="" a="" wide="" class="" of="" problems="" in="" mathematical="" physics.="" asymptotics="" this="" type="" were="" constructed="" recently="" many="" linear="" _probc2ad_="" lems="" _physics3b_="" certain="" specific="" formulas="" obtained="" by="" _differc2ad_="" ent="" methods="" _28_v.="" m.="" babich="" _5b_5="" _-75d_2c_="" v.="" p.="" lazutkin="" _5b_765d_2c_="" a.="" _sokolov2c_="" 1.="" _terc2ad_="" nov="" _5b_1135d_2c_="" j.="" schwinger="" _5b_1072c_="" _1085d_2c_="" e.="" heller="" _5b_535d_2c_="" g.="" hagedorn="" _5b_502c_="" _515d_2c_="" n.="" _bayer2c_="" katkov="" _5b_215d_2c_="" chernikov="" _5b_355d_="" _others29_.="" _however2c_="" general="" _28_hamiltonian29_="" formalism="" obtaining="" is="" clearly="" _required3b_="" state="" affairs="" expressed="" both="" recent="" physical="" literature.="" _example2c_="" editors="" collected="" volume="" _5b_1065d_="" write="" its="" _preface3a_="" _22_one="" can="" hope="" that="" near="" future="" computational="" _proc2ad_="" cedure="" fields="" with="" complex="" _phase2c_="" similar="" to="" usual="" one="" real="" will="" be="">
Title:The Complex WKB Method for Nonlinear Equations I: Linear TheoryFormat:PaperbackDimensions:304 pages, 23.5 × 15.5 × 0.02 inPublished:October 6, 2012Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034896697

ISBN - 13:9783034896696

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Table of Contents

I. Equations and problems of narrow beam mechanics.- II. Hamiltonian formalism of narrow beams.- III. Approximate solutions of the nonstationary transport equation.- IV. Stationary Hamilton-Jacobi and transport equations.- V. Complex Hamiltonian formalism of compact (cyclic) beams.- VI. Canonical operators on Lagrangian manifolds with complex germ and their applications to spectral problems of quantum mechanics.- References.- Appendix A Complex germ generated by a linear connection.- Appendix B Asymptotic solutions with pure imaginary phase and the tunnel equation.- Appendix C Analytic asymptotics of oscillatory decreasing type (heuristic considerations).