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This book is devoted to one of the most interesting and rapidly
developing areas of modern nonlinear physics and mathematics -
theoretical, analytical andnumerical,
studyofthestructureanddynamicsofone-dimensionalaswell as two- and
three-dimensional solitons and nonlinear wave packets described by
the Korteweg-de Vries (KdV), Kadomtsev-Petviashvili (KP), nonlinear
Schr] odinger (NLS) and derivative nonlinear Schr] odinger (DNLS)
classes of equations. Special attention is paid to generalizations
(relevant to various complex physical media) of these equations,
accounting for higher-order d- persion corrections, in?uence of
dissipation, instabilities, and stochastic ?- tuations of the wave
?elds. We present here a coordinated approach to the theory,
simulations, and applications of the nonlinear one-, two-, and
three-dimensional solitary wave solutions. Overall, the content of
the book is a systematic account of results
notonlyalreadyknownintheliterature,
butalsothoseofneworiginalstudies related to the theory of models
allowing soliton solutions, and analyses of the stability and
asymptotics of these solutions. We give signi?cant consideration to
numerical methods and results of numerical simulations of the
structure and dynamics of solitons and nonlinear wave packets.
Together with deep insights into the theory, applications to
various branches of modern physics are considered, especially to
plasma physics (such as space plasmas including ionospheric and
magnetospheric processes), hydrodynamics, and atmosphere dynamics.
Presently, thetheoryofone-dimensionalnonlinearequationsoftheclasses
consideredbytheauthorsiswelldeveloped, andtheprogressinstudiesofthe
structure and evolution of one-dimensional solitons and wave
packets is ob- ous. This progress was especially fast after the
discovery of hidden algebraic symmetries of the KdV, NLS, and other
(integrable by the inverse scatt- ing transform (IST) method)
classes of one-dimensional evolution equations
This book is devoted to one of the most interesting and rapidly
developing areas of modern nonlinear physics and mathematics -
theoretical, analytical andnumerical,
studyofthestructureanddynamicsofone-dimensionalaswell as two- and
three-dimensional solitons and nonlinear wave packets described by
the Korteweg-de Vries (KdV), Kadomtsev-Petviashvili (KP), nonlinear
Schr] odinger (NLS) and derivative nonlinear Schr] odinger (DNLS)
classes of equations. Special attention is paid to generalizations
(relevant to various complex physical media) of these equations,
accounting for higher-order d- persion corrections, in?uence of
dissipation, instabilities, and stochastic ?- tuations of the wave
?elds. We present here a coordinated approach to the theory,
simulations, and applications of the nonlinear one-, two-, and
three-dimensional solitary wave solutions. Overall, the content of
the book is a systematic account of results
notonlyalreadyknownintheliterature,
butalsothoseofneworiginalstudies related to the theory of models
allowing soliton solutions, and analyses of the stability and
asymptotics of these solutions. We give signi?cant consideration to
numerical methods and results of numerical simulations of the
structure and dynamics of solitons and nonlinear wave packets.
Together with deep insights into the theory, applications to
various branches of modern physics are considered, especially to
plasma physics (such as space plasmas including ionospheric and
magnetospheric processes), hydrodynamics, and atmosphere dynamics.
Presently, thetheoryofone-dimensionalnonlinearequationsoftheclasses
consideredbytheauthorsiswelldeveloped, andtheprogressinstudiesofthe
structure and evolution of one-dimensional solitons and wave
packets is ob- ous. This progress was especially fast after the
discovery of hidden algebraic symmetries of the KdV, NLS, and other
(integrable by the inverse scatt- ing transform (IST) method)
classes of one-dimensional evolution equations
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