Articles written in Pramana – Journal of Physics
Volume 90 Issue 4 April 2018 Article ID 0045 Research Article
Bäcklund transformation and soliton solutions in terms of the Wronskian for the Kadomtsev–Petviashvili-based system in fluid dynamics
ZHONG DU BO TIAN XI-YANG XIE JUN CHAI XIAO-YU WU
In this paper, investigation is made on a Kadomtsev–Petviashvili-based system, which can be seen in fluid dynamics, biology and plasma physics. Based on the Hirota method, bilinear form and Bäcklund transformation(BT) are derived. $N$-soliton solutions in terms of the Wronskian are constructed, and it can be verified that the $N$ soliton solutions in terms of the Wronskian satisfy the bilinear form and Bäcklund transformation. Through the $N$-soliton solutions in terms of the Wronskian, we graphically obtain the kink-dark-like solitons and parallel solitons, which keep their shapes and velocities unchanged during the propagation.
Volume 91 Issue 3 September 2018 Article ID 0043 Research Article
Lumps and rouge waves for a (3 + 1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation in fluid mechanics
YING YIN BO TIAN HAN-PENG CHAI YU-QIANG YUAN ZHONG DU
In this paper, a (3 + 1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation, which describes the long water waves and small-amplitude surface waves with the weak nonlinearity, weak dispersionand weak perturbation in fluid mechanics, is investigated. Lump, lump–soliton and rouge–soliton solutions are obtained with the aid of symbolic computation. For the lump and soliton, amplitudes are related to the nonlinearity coefficient and dispersion coefficient, while velocities are related to the perturbation coefficients. Fusion and fission phenomena between the lump and soliton are observed, respectively. Graphic analysis shows that: (i) soliton’s amplitude becomes larger after the fusion interaction, and becomes smaller after the fission interaction; (ii) afterthe interaction, the soliton propagates along the opposite direction to before when any one of the perturbation coefficients is a time-dependent function. For the interactions between the rogue wave and two solitons, the roguewave splits from one soliton and merges into the other one, and the two solitons exchange the amplitudes through the energy transfer by the rogue wave.
Volume 92 Issue 1 January 2019 Article ID 0009 Research Article
Semirational rogue waves for the three coupled variable-coefficient nonlinear Schrödinger equations in an inhomogeneous multicomponent optical fibre
HAN-PENG CHAI BO TIAN JUN CHAI ZHONG DU
In this paper, we investigate the three coupled variable-coefficient nonlinear Schrödinger equations, which describe the amplification or attenuation of the picosecond pulse propagation in the inhomogeneous multicomponent optical fibre with different frequencies or polarisations. Based on the Darboux dressing transformation, semirational rogue wave solutions are derived. Semirational rogue waves, Peregrine combs and Peregrine walls are obtained and demonstrated. Splitting behaviour of the semirational Peregrine combs and attenuating phenomenon of the semirational Peregrine wall are exhibited. Effects of the group velocity dispersion, nonlinearity and fibre gain/loss are discussed according to the different fibres.We find that the maximum amplitude of the hump of the semirational rogue wave is less than nine times the background height due to the interaction between the soliton part and rogue wave part. Further, there is a bent in the soliton part of the semirational rogue.
Volume 97, 2023
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