Under investigation in this paper is a complex modified Korteweg–de Vries(KdV) equation, which describes the propagation of short pulses in optical fibers. Bilinear forms and multi-soliton solutions are obtained thro...Under investigation in this paper is a complex modified Korteweg–de Vries(KdV) equation, which describes the propagation of short pulses in optical fibers. Bilinear forms and multi-soliton solutions are obtained through the Hirota method and symbolic computation. Breather-like and bound-state solitons are constructed in which the signs of the imaginary parts of the complex wave numbers and the initial separations of the two parallel solitons are important factors for the interaction patterns. The periodic structures and position-induced phase shift of some solutions are introduced.展开更多
In this paper, by using bilinear form and extended three-wave type of ans¨atz approach, we obtain new cross-kink multi-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation, including the periodic breath...In this paper, by using bilinear form and extended three-wave type of ans¨atz approach, we obtain new cross-kink multi-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation, including the periodic breather-type of kink three-soliton solutions, the cross-kink four-soliton solutions, the doubly periodic breathertype of soliton solutions and the doubly periodic breather-type of cross-kink two-soliton solutions. It is shown that the generalized three-wave method, with the help of symbolic computation, provides an effective and powerful mathematical tool for solving high dimensional nonlinear evolution equations in mathematical physics.展开更多
The coupled modified nonlinear Schrodinger equations are under investigation in this work. Starting from analyzing the spectral problem of the Lax pair, a Riemann-Hilbert problem for the coupled modified nonlinear Sch...The coupled modified nonlinear Schrodinger equations are under investigation in this work. Starting from analyzing the spectral problem of the Lax pair, a Riemann-Hilbert problem for the coupled modified nonlinear Schrodinger equations is formulated. And then, through solving the obtained Riemann-Hilbert problem under the conditions of irregularity and reflectionless case, N-soliton solutions for the equations are presented. Furthermore, the localized structures and dynamic behaviors of the one-soliton solution are shown graphically.展开更多
Head-on collisions among the single-and multi-soliton’s heavy ion acoustic waves(HIAWs) of multi-ion plasma are studied. The plasma consists of adiabatic positively charged inertial heavy ions, Boltzmann energy distr...Head-on collisions among the single-and multi-soliton’s heavy ion acoustic waves(HIAWs) of multi-ion plasma are studied. The plasma consists of adiabatic positively charged inertial heavy ions, Boltzmann energy distributed light ions and kappa energy distributed electrons. The extended poincaré-Lighthill-Kuo(e PLK) method is applied for the derivation of two-sided Korteweg–de Vries(KdV) equations(KdVEs). The KdV single-soliton solutions(KdVSSs) are determined using the hyperbolic secant method and the KdV multi-soliton solutions(KdVMSs)are obtained using the Hirota method. The effects of superthermality of electrons, temperature ratios of electron to light ion and heavy ion to electron, and the density ratio of electron to heavy ion on phase shifts are investigated for the head-on collisions between two-soliton HIAWs. The effects of plasma parameters on angular frequency, phase speed, production of multi-soliton structures, and the head-on collisions among single-, double-, triple-, quadruple-, and quintuplesolitons are also studied.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 12161061)the Fundamental Research Funds for the Inner Mongolia University of Finance and Economics (Grant No. NCYWT23036)+2 种基金the Young Innovative and Entrepreneurial Talents of the Inner Mongolia Grassland Talents Project in 2022,Autonomous Region “Five Major Tasks” Research Special Project for the Inner Mongolia University of Finance and Economics in 2024 (Grant No. NCXWD2422)High Quality Research Achievement Cultivation Fund for the Inner Mongolia University of Finance and Economics in 2024 (Grant No. GZCG2426)the Talent Development Fund of Inner Mongolia Autonomous Region, China。
文摘Under investigation in this paper is a complex modified Korteweg–de Vries(KdV) equation, which describes the propagation of short pulses in optical fibers. Bilinear forms and multi-soliton solutions are obtained through the Hirota method and symbolic computation. Breather-like and bound-state solitons are constructed in which the signs of the imaginary parts of the complex wave numbers and the initial separations of the two parallel solitons are important factors for the interaction patterns. The periodic structures and position-induced phase shift of some solutions are introduced.
文摘In this paper, by using bilinear form and extended three-wave type of ans¨atz approach, we obtain new cross-kink multi-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation, including the periodic breather-type of kink three-soliton solutions, the cross-kink four-soliton solutions, the doubly periodic breathertype of soliton solutions and the doubly periodic breather-type of cross-kink two-soliton solutions. It is shown that the generalized three-wave method, with the help of symbolic computation, provides an effective and powerful mathematical tool for solving high dimensional nonlinear evolution equations in mathematical physics.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61072147 and 11271008)
文摘The coupled modified nonlinear Schrodinger equations are under investigation in this work. Starting from analyzing the spectral problem of the Lax pair, a Riemann-Hilbert problem for the coupled modified nonlinear Schrodinger equations is formulated. And then, through solving the obtained Riemann-Hilbert problem under the conditions of irregularity and reflectionless case, N-soliton solutions for the equations are presented. Furthermore, the localized structures and dynamic behaviors of the one-soliton solution are shown graphically.
文摘Head-on collisions among the single-and multi-soliton’s heavy ion acoustic waves(HIAWs) of multi-ion plasma are studied. The plasma consists of adiabatic positively charged inertial heavy ions, Boltzmann energy distributed light ions and kappa energy distributed electrons. The extended poincaré-Lighthill-Kuo(e PLK) method is applied for the derivation of two-sided Korteweg–de Vries(KdV) equations(KdVEs). The KdV single-soliton solutions(KdVSSs) are determined using the hyperbolic secant method and the KdV multi-soliton solutions(KdVMSs)are obtained using the Hirota method. The effects of superthermality of electrons, temperature ratios of electron to light ion and heavy ion to electron, and the density ratio of electron to heavy ion on phase shifts are investigated for the head-on collisions between two-soliton HIAWs. The effects of plasma parameters on angular frequency, phase speed, production of multi-soliton structures, and the head-on collisions among single-, double-, triple-, quadruple-, and quintuplesolitons are also studied.
基金Supported by the Natural Science Foundation of Henan Province of China(0111050200) Natural Science Foundation of Education Committee of Henan Province of China(2003110003)the Science Foundation of Henan University of Science and Technology(2003ZY03)
基金National Natural Science Foundation of China(No.11304409)Nature Science Foundation of Chongqing(No.cstc2018jcyjA0655)Science and Technology Commission Project of Chongqing(No.cstc2017zdcy-zdzxX0011)。
基金the National Key Basic Research Development of China (Grant No. 1998030600) the National Nature Science Foundation of China (Grant No. 10072013.10072189)
