ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The Lax conjecture for the KdV equation ut+6uux+uxxx=0 is proved. Let u be the solution of the KdV equation, which is defined for all x and t and vanishes at x=±∞. Then there exist a discrete set of positive numbers c1,...,cN —called the eigenspeeds of u—and sets of phase shifts θ±j such that limt→±∞ u(x+ct,t) ={S(x−θ±j,cj),0, if c=cj,if c≠cj, where S is a solitary wave [P. D. Lax, Commun. Pure Appl. Math. 21, 467 (1968)].
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.528074
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