CONSTRUCTION OF NEW DYNAMICAL SYSTEMS WHILE PRESERVING AN INTEGRAL
Basically, integrable dynamical system is a system that can be solved analytically. It is because of the existence of functions called integral, which can reduce the system. After the discovery of soliton phenomenon in Korteweg-de Vries equation, many theories on integrable systems have been growing...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/31088 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Basically, integrable dynamical system is a system that can be solved analytically. It is because of the existence of functions called integral, which can reduce the system. After the discovery of soliton phenomenon in Korteweg-de Vries equation, many theories on integrable systems have been growing up until now. Some methods used in continuous systems is implemented to learn discrete version of the systems, for example: travelling wave solution and Lax pair of matrices. <br />
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The aim of this thesis is constructing new discrete dynamical systems from a given system of ordinary difference equations while preserving an integral. Hence, there are two things that need to be introduced. The first one is standard staircase method as a discrete travelling wave solution, and the second one is consistency around the cube as a method to find Lax pair of an integrable system. These two will be used for defining monodromy matrix which later open a way to find explicit formula for integral(s) of the system. <br />
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