Optical solitons and conservation laws with generalized Kudryashov's law of refractive index.

• The newly proposed generalized Kudryashov's law of refractive index is considered. • Dark, bright and singular optical soliton solutions are revealed. • Extended generalized Kudryashov's method and an addendum to Kudryashov's approach are implemented. • The conservation laws are also enumerated. This paper addresses the newly proposed generalized Kudryashov's law of refractive index to obtain dark, bright and singular optical soliton solutions. Two approaches that collectively reveal such soliton solutions are extended generalized Kudryashov's method and an addendum to Kudryashov's approach. Finally, the conservation laws are also enumerated. [ABSTRACT FROM AUTHOR]