Different Kinds of Singular and Nonsingular Exact Traveling Wave Solutions of the Kudryashov-Sinelshchikov Equation in the Special Parametric Conditions

Figure 5

The profile of soliton solutions (25) for (a) 𝛼=−0.5,𝜆=2, and 𝑐=−1.0001, (b) 𝛼=−0.5,𝜆=2, and 𝑐=−1.2, and (c) 𝛼=−0.5,𝜆=2, and 𝑐=−1.25, and (d) 𝛼=−0.5,𝜆=2, and 𝑐=−1.25000001.

(a) Broken wave

(b) Broken loop soliton

(c) Dark loop soliton

(d) Smooth-bright soliton