Generalizations of the Wave Equation
نویسندگان
چکیده
منابع مشابه
Generalizations of the Wave Equation
The main result of this paper is a generalization of the property that, for smooth u, uxy = 0 implies (*) u(x, y) = a(x) + b(y). Any function having generalized unsymmetric mixed partial derivative identically zero is of the form (*). There is a function with generalized symmetric mixed partial derivative identically zero not of the form (*), but (*) does follow here with the additional assumpt...
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We generalize the KPZ equation to an O(3) N = 2j + 1 component model. In the limit N → ∞ we show that the mode coupling equations become exact. Solving these approximately we find that the dynamic exponent z increases from 3/2 for d = 1 to 2 at the dimension d ≈ 3.6. For d = 1 it can be shown analytically that z = 3/2 for all j. The case j = 2 for d = 2 is investigated by numerical integration ...
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The linear stability problem for solitary wave states of the Kawahara—or fifthorder KdV-type—equation and its generalizations is considered. A new formulation of the stability problem in terms of the symplectic Evans matrix is presented. The formulation is based on a multisymplectification of the Kawahara equation, and leads to a new characterization of the basic solitary wave, including change...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1993
ISSN: 0002-9947
DOI: 10.2307/2154444