Abstract
In this manuscript, we utilize the algorithm of
(
G
′
/
G
)
expansion method to construct new solutions of three important models, the Ablowitz–Kaup–Newell–Segur water wave equation, the
(
2
+
1
)
-dimensional Boussinesq equation, and the
(
3
+
1
)
-dimensional Yu–Toda–Sasa–Fukuyama equation, having numerous application in plasma physics, fluid dynamics, and optical fibers. Some new types of traveling wave solutions are acquired, which have not been obtained previously by using this our new technique. The achieved solutions appear with all necessary constraint conditions, which are compulsory for them to exist. The constructed new solutions have vital applications in applied sciences. To understand the physical phenomena of these models, we have also presented graphically movements of the obtained results. It is shown that the our technique provides a more powerful mathematical tool for constructing exact traveling wave solutions for many other nonlinear waves models in mathematics and physics.