Generalized solutions and Euler - Darboux transformations
Обобщенные решения и преобразования Эйлера - Дарбу

Igor' Viktorovich Verevkin
2014 Ufimskii Matematicheskii Zhurnal  
We introduce Euler-Darboux transformation for non-homogeneous differential equations with the right-hand side being a generalized function. As an example, we construct the fundamental solutions for Klein-Gordon-Fock and Schrödinger equations with variable coefficients describing a particle in external scalar field.
doi:10.13108/2014-6-4-60 fatcat:smelpbg3ufatvbj4wbftaqutte