The(2+1)-dimensional integrable generalization of the Gardner(2DG)equation is solved via the inverse scattering transform method in this paper.A kind of general solution of the equation is obtained by introducing long...The(2+1)-dimensional integrable generalization of the Gardner(2DG)equation is solved via the inverse scattering transform method in this paper.A kind of general solution of the equation is obtained by introducing long derivatives V_(x),V_(y),V_(t).Two different constraints on the kernel function K are introduced under the reality of the solution u of the 2DG equation.Then,two classes of exact solutions with constant asymptotic values at infinity u|x^(2)+y^(2)→∞→0 are constructed by means of the∂¯-dressing method for the casesσ=1 andσ=i.The rational and multiple pole solutions of the 2DG equation are obtained with the kernel functions of zero-order and higher-order Dirac delta functions,respectively.展开更多
The(2+1)-dimensional integrable generalization of the Kaup-Kuper-shmidt(KK)equation is solved by the inverse spectral transform method in this paper.Several new long derivative operators V_(x),V_(y) and V_(t) and the ...The(2+1)-dimensional integrable generalization of the Kaup-Kuper-shmidt(KK)equation is solved by the inverse spectral transform method in this paper.Several new long derivative operators V_(x),V_(y) and V_(t) and the kernel functions K of ■-problem are introduced to construct a type of general solution of the KK equation.Based on these,several classes of the new exact solutions,with constant asymptotic values at infinity u|_(x^(2)+y^(2)→∞)→0,for the KK equation are constructed via the-dressing method.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1237125611971475)。
文摘The(2+1)-dimensional integrable generalization of the Gardner(2DG)equation is solved via the inverse scattering transform method in this paper.A kind of general solution of the equation is obtained by introducing long derivatives V_(x),V_(y),V_(t).Two different constraints on the kernel function K are introduced under the reality of the solution u of the 2DG equation.Then,two classes of exact solutions with constant asymptotic values at infinity u|x^(2)+y^(2)→∞→0 are constructed by means of the∂¯-dressing method for the casesσ=1 andσ=i.The rational and multiple pole solutions of the 2DG equation are obtained with the kernel functions of zero-order and higher-order Dirac delta functions,respectively.
基金supported by the National Natural Science Foundation of China(Grant Nos.12371256,11971475).
文摘The(2+1)-dimensional integrable generalization of the Kaup-Kuper-shmidt(KK)equation is solved by the inverse spectral transform method in this paper.Several new long derivative operators V_(x),V_(y) and V_(t) and the kernel functions K of ■-problem are introduced to construct a type of general solution of the KK equation.Based on these,several classes of the new exact solutions,with constant asymptotic values at infinity u|_(x^(2)+y^(2)→∞)→0,for the KK equation are constructed via the-dressing method.
