The Direct Method in Soliton Theory [Hardcover]

Account of method of solving soliton equations by the inventor of the method.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. The main part of this book concerns the more modern version of the method. 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, and will be essential for all those working in soliton theory.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. The main part of this book concerns the more modern version of the method. 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, and will be essential for all those working in soliton theory.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 complex calculations of the inverse scattering transform. This analysis is essentially concerned with the more modern version of the method. Still maintaining the original philosophy of using relatively simple mathematics, the method has, nevertheless, been influenced by the work of the Kyoto school, and will be essential for all working in soliton theory.Preface; Foreword; 1. Bilinearization of soliton equations; 2. Determinants and pfaffians; 3. Structure of soliton equations; 4. B?cklund transformations; Afterword; References; Index. The best available introduction to the direct method to be found in the literature, adding essential insight to what may be found elsewhlÃ&