Akademik Veri Yönetim Sistemi
Encyclopedia of Complexity and Systems Science, Mohamed Atef Helal, Editör, Springer Nature, New York, ss.139-159, 2022
Nonlinear phenomena play a crucial role in applied mathematics and physics. Calculating exact and numerical solutions,
in particular, traveling wave solutions, of nonlinear PDEs in mathematical physics plays an important role in soliton theory.
Moreover, these equations are mathematical models of complex physical occurrences that arise in engineering,
chemistry, biology, mechanics, and physics.
In this work, we give a brief history of the above-mentioned nonlinear equations and how this type of equation has led to
the soliton solutions; we then present an introduction to the theory of solitons. Soliton theory is an important branch of
applied mathematics and mathematical physics. In the last decade this topic has become an active and productive area
of research, and applications of the soliton equations in physical cases have been considered. These have important
applications in fluid mechanics, nonlinear optics, ion plasma, classical and quantum fields' theories etc.