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A New Class of Soliton Solutions for the (Modified) Kadomtsev‐Petviashvili Equation
Author(s) -
Renger Walter
Publication year - 1999
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19992020110
Subject(s) - kadomtsev–petviashvili equation , mathematics , soliton , class (philosophy) , mathematical analysis , mathematical physics , pure mathematics , partial differential equation , nonlinear system , characteristic equation , physics , quantum mechanics , artificial intelligence , computer science
We construct solutions of the Kadomtsev‐Petviashvili equation and its counterpart, the modified Kadomtsev‐Petviashvili equation, with an infinite number of solitons by a careful examination of the limits of N‐ soliton solutions as N → ∞ . We give sufficient conditions to ensure that these limits exist and satisfy the (modified) Kadomtsev‐Petviashvili equation.