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Classes of Linearisable Hierarchies of Evolution Equations in (1+1) Dimensions
2002 (English)Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

This thesis is based on eight classes of linearisable second order evolution equations in (1+1) dimension with known linearisations. These classes are linearised by the x-generalised hodograph transformation and was first presented in the recent article "A Tree of Linearisable Second-Order Evolution Equations", J. Nonlin. Math. Phys. 8 (2001), 342-362 by N. and M. Euler. Here we present corresponding hierarchies of higher order evolution equations evolved from these eight classes. With symmetry methods, six new recursion operators where developed to construct such hierarchies. We also show that every equation in each hierarchy can be linearised by the same transformation that linearises the corresponding second order equation. These classes are further extended by writing the equations in potential form. This leads to new classes of linerarisable hierarchies and more recursion operators.

Place, publisher, year, edition, pages
Keyword [en]
Technology, recursion operators, evolution, differential equations, linearisable potential
Keyword [sv]
URN: urn:nbn:se:ltu:diva-43183ISRN: LTU-EX--02/280--SELocal ID: 11321b66-1adc-4fc1-af09-25eaabdd68c2OAI: diva2:1016412
Subject / course
Student thesis, at least 30 credits
Educational program
Engineering Physics, master's level
Validerat; 20101217 (root)Available from: 2016-10-04 Created: 2016-10-04Bibliographically approved

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