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On the Kadomtsev‐Petviashvili Equation and Associated Constraints
Author(s) -
Ablowitz Mark J.,
Villarroel Javier
Publication year - 1991
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1991853195
Subject(s) - kadomtsev–petviashvili equation , mathematics , mathematical analysis , mathematical physics , physics , partial differential equation , burgers' equation
The initial‐boundary‐value problem for the Kadomtsev‐Petviashvili equation in infinite space is considered. When formulated as an evolution equation, found that a symmetric integral is the appropriate choice in the nonlocal term; namely, . If one simply chooses , then an infinite number of constraints on the initial data in physical space are required, the first being . The conserved quantities are calculated, and it is shown that they must be suitably regularized from those that have been used when the constraints are imposed.