In this paper, a uniform analysis of the asymptotic properties of high frequencies of non-uniform bars, beams and circular membranes is given by using perturbation method, and the ease of discontinuous physical parame...In this paper, a uniform analysis of the asymptotic properties of high frequencies of non-uniform bars, beams and circular membranes is given by using perturbation method, and the ease of discontinuous physical parameters is also discussed.展开更多
In this paper,the bilinear formalism,bilinear B?cklund transformations and Lax pair of the(2+1)-dimensional KdV equation are constructed by the Bell polynomials approach.The N-soliton solution is derived directly from...In this paper,the bilinear formalism,bilinear B?cklund transformations and Lax pair of the(2+1)-dimensional KdV equation are constructed by the Bell polynomials approach.The N-soliton solution is derived directly from the bilinear form.Especially,based on the two-soliton solution,the lump solution is given out analytically by taking special parameters and using Taylor expansion formula.With the help of the multidimensional Riemann theta function,multiperiodic(quasiperiodic)wave solutions for the(2+1)-dimensional KdV equation are obtained by employing the Hirota bilinear method.Moreover,the asymptotic properties of the one-and two-periodic wave solution,which reveal the relations with the single and two-soliton solution,are presented in detail.展开更多
文摘In this paper, a uniform analysis of the asymptotic properties of high frequencies of non-uniform bars, beams and circular membranes is given by using perturbation method, and the ease of discontinuous physical parameters is also discussed.
基金supported by the National Natural Science Foundation of China(No.12175069 and No.12235007)Science and Technology Commission of Shanghai Municipality(No.21JC1402500 and No.22DZ2229014)。
文摘In this paper,the bilinear formalism,bilinear B?cklund transformations and Lax pair of the(2+1)-dimensional KdV equation are constructed by the Bell polynomials approach.The N-soliton solution is derived directly from the bilinear form.Especially,based on the two-soliton solution,the lump solution is given out analytically by taking special parameters and using Taylor expansion formula.With the help of the multidimensional Riemann theta function,multiperiodic(quasiperiodic)wave solutions for the(2+1)-dimensional KdV equation are obtained by employing the Hirota bilinear method.Moreover,the asymptotic properties of the one-and two-periodic wave solution,which reveal the relations with the single and two-soliton solution,are presented in detail.
