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##### This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

Adem, Abdullahi Rashid Yildirim, Yakup and Yaşar, Emrullah 2019. Soliton solutions to the non-local Boussinesq equation by multiple exp-function scheme and extended Kudryashov’s approach. Pramana, Vol. 92, Issue. 2,

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Paul, G C Rashedunnabi, A H M and Haque, M D 2019. Testing efficiency of the generalised $$\left( {{{G}'}/G} \right)$$G′/G-expansion method for solving nonlinear evolution equations. Pramana, Vol. 92, Issue. 2,

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Hafez, M. G. 2019. Face to Face Collisions of Ion Acoustic Multi-Solitons and Phase Shifts in a Dense Plasma. Brazilian Journal of Physics,

Trejo-Garcia, David Gonzalez-Hernandez, Diana López-Aguayo, Daniel and Lopez-Aguayo, Servando 2018. Stable Hermite-Gaussian solitons in optical lattices. Journal of Optics, Vol. 20, Issue. 12, p. 125501.

Wang, Bao Chang, Xiang-Ke Hu, Xing-Biao and Li, Shi-Hao 2018. On moving frames and Toda lattices of BKP and CKP types. Journal of Physics A: Mathematical and Theoretical, Vol. 51, Issue. 32, p. 324002.

Liu, Wei and Li, Xiliang 2018. General soliton solutions to a $$\varvec{(2+1)}$$(2+1)-dimensional nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions. Nonlinear Dynamics, Vol. 93, Issue. 2, p. 721.

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Guo, Ding and Tian, Shou-Fu 2018. Stability analysis, soliton waves, rogue waves and interaction phenomena for the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation. Modern Physics Letters B, Vol. 32, Issue. 28, p. 1850345.

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#### Book description

The bilinear, or Hirota's direct, method was invented in the early 1970s as an elementary means of constructing soliton solutions that avoided the use of the heavy machinery of the inverse scattering transform and was successfully used to construct the multisoliton solutions of many new equations. In the 1980s the deeper significance of the tools used in this method - Hirota derivatives and the bilinear form - came to be understood as a key ingredient in Sato's theory and the connections with affine Lie algebras. The main part of this book concerns the more modern version of the method in which solutions are expressed in the form of determinants and pfaffians. While maintaining the original philosophy of using relatively simple mathematics, it has, nevertheless, been influenced by the deeper understanding that came out of the work of the Kyoto school. The book will be essential for all those working in soliton theory.

#### Reviews

'Overall, the book under review is a concise and essentially self-contained book, written by one of the leading researchers associated with the development of soliton theory … provides an interesting insight into the development of a straight forward method for obtaining exact solutions for wide classes of nonlinear equations.'

Peter Clarkson - University of Kent

' … a nice example of a mathematical writing that can be read at nearly normal pace, which is extremely rare nowadays.'

Source: Zentralblatt MATH

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