A linear superposition principle of exponential traveling waves is analyzed for Hirota bilinear equations, with an aim to construct a specific sub-class of N-soliton solutions formed by linear combinations of exponential traveling waves. Applications are made for the 3 + 1 dimensional KP, Jimbo–Miwa and BKP equations, thereby presenting their particular N-wave solutions. An opposite question is...

We introduce a class of reductions the two-component KP hierarchy, which includes Hirota-Ohta system hierarchy. The description reduced hierarchies is based on Hirota bilinear identity and an extra relation characterising reduction. derive reduction conditions in terms Lax operator higher linear operators as well basic equations.

This paper concerns the iterative solution of the linear system arising from the Chebyshev–collocation approximation of second-order elliptic equations and presents an optimal multigrid preconditioner based on alternating line Gauss–Seidel smoothers for the corresponding stiffness matrix of bilinear finite elements on the Chebyshev–Gauss–Lobatto grid.  2000 IMACS. Published by Elsevier Science...

A non-linear modelling technique is presented which uses a non-parametric bilinear representation in the form of a linear and a series of bilinear impulse coefficients. The technique is applied in simulation to the identification of a non-linear continuous stirred tank reactor (CSTR) and the resulting model is shown to satisfy correlation based non-linear validity tests. It is also compared wit...

We study a simple nonlinear model defined on the honeycomb and triangular lattices. propose bilinearization scheme for field equations demonstrate that resulting system is closely related to well-studied integrable models, such as Hirota bilinear difference equation Ablowitz-Ladik system. This result used derive two sets of explicit solutions: N-soliton solutions ones constructed Toeplitz deter...

As an application of Hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. We have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear Backlund transformations and construction of ...

This paper considers the optimal control problem for time-delay bilinear systems affected by sinusoidal disturbances with known frequency and measurable amplitude and phase. Firstly, using the differential homeomorphism, a timedelay bilinear system affected by sinusoidal disturbances is changed to a time-delay pseudo linear system through the coordinate transformation. Then the system with time...