Bilinear equations, Bell polynomials and linear superposition principle
نویسندگان
چکیده
منابع مشابه
Bilinear equations, Bell polynomials and linear superposition principle
A class of bilinear differential operators is introduced through assigning appropriate signs and used to create bilinear differential equations which generalize Hirota bilinear equations. The resulting bilinear differential equations are characterized by a special kind of Bell polynomials and the linear superposition principle is applied to the construction of their linear subspaces of solution...
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A linear superposition principle of exponential traveling waves is analyzed for Hirota bilinear equations, with an aim to construct a specific sub-class of N-soliton solutions formed by linear combinations of exponential traveling waves. Applications are made for the 3 + 1 dimensional KP, Jimbo–Miwa and BKP equations, thereby presenting their particular N-wave solutions. An opposite question is...
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A class of trilinear differential operators is introduced through a technique of assigning signs to derivatives and used to create trilinear differential equations. The resulting trilinear differential operators and equations are characterized by the Bell polynomials, and the superposition principle is applied to the construction of resonant solutions of exponential waves. Two illustrative exam...
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Several nonlinear systems such as the Korteweg-de Vries (KdV) and modified KdV equations and lambda phi(4) theory possess periodic traveling wave solutions involving Jacobi elliptic functions. We show that suitable linear combinations of these known periodic solutions yield many additional solutions with different periods and velocities. This linear superposition procedure works by virtue of so...
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Letting Bn,r be the n-th r-Bell polynomial, it is well known that Bn(x) admits specific integer coordinates in the two bases {x}i and {xBi(x)}i according to, respectively, the Stirling numbers and the binomial coefficients. Our aim is to prove that the sequences Bn+m,r(x) and Bn,r+s(x) admit a binomial recurrence coefficient in different bases of the Q-vector space formed by polynomials of Q[X].
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ژورنال
عنوان ژورنال: Journal of Physics: Conference Series
سال: 2013
ISSN: 1742-6596
DOI: 10.1088/1742-6596/411/1/012021