The interaction of an oblique line soliton with a one-dimensional dynamic mean flow is analyzed using the Kadomtsev-Petviashvili II (KPII) equation. Building upon previous studies that examined transmission or trapping by slowly varying rarefaction oscillatory dispersive shock wave in one space and time dimension, this paper allows for incident to approach changing at nonzero angle. By deriving...

We have recently solved the inverse scattering problem for oneparameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev Petviashvili (dKP) equation. We showed, in particu...

We derive the Kadomtsev-Petviashvili (KP) equation defined over a general associative algebra and construct its N -soliton solution. For the example of the Moyal algebra, we find multi-soliton solutions for arbitrary space-space noncommutativity. The noncommutativity of coordinates is shown to obstruct the general construction of a τ function for these solitons. We investigate the two-soliton s...

In this paper, a new (2 + 1)-dimensional nonlinear evolution equation is investigated. This called the Kadomtsev–Petviashvili–Sawada–Kotera–Ramani equation, which can be seen as two-dimensional extension of Korteweg–de Vries–Sawada–Kotera–Ramani equation. By means Hirota’s bilinear operator and binary Bell polynomials, form Bäcklund transformation are obtained. Furthermore, by application Hopf-...

In the previous papers (notably, Y. Kodama, J. Phys. A 37, 11169-11190 (2004), and G. Biondini and S. Chakravarty, J. Math. Phys. 47 033514 (2006)), we found a large variety of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation. The line-soliton solutions are solitary waves which decay exponentially in (x,y)-plane except along certain rays. In this paper, we show that those...