A ($$1+1$$1+1)-dimensional inhomogeneous cubic–quintic–septimal nonlinear Schrödinger equation with $$\mathcal {PT}$$PT-symmetric potentials is studied, and two families of soliton solutions are obtained. From soliton solutions, the amplitude of soliton is independent… Click to show full abstract
A ($$1+1$$1+1)-dimensional inhomogeneous cubic–quintic–septimal nonlinear Schrödinger equation with $$\mathcal {PT}$$PT-symmetric potentials is studied, and two families of soliton solutions are obtained. From soliton solutions, the amplitude of soliton is independent of the $$\mathcal {PT}$$PT-symmetric potential parameter k; however, the phase depends on the parameter k. The phase of soliton alters from negative to positive values at the location of center. Moreover, the evolutional behaviors of these solitons are discussed.
               
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