<p>Nonlinear optical fibers are supposed as one of the effective transmission media which can be applied in the optical fiber communication. A Lax-integrable (2+1)-dimensional Kundu-Mukherjee-Naskar equation, which describes the propagation of optical pulses in a nonlinear optical fiber, is investigated in this paper. We first construct the <i>N</i>-fold binary Darboux transformation, where <i>N</i> is a positive integer. Via the obtained <i>N</i>-fold binary Darboux transformation, we derive the <i>N</i>-soliton solutions and perform the asymptotic analysis on the obtained <i>N</i>-soliton solutions. The <i>N</i>-soliton solutions can be decomposed into <i>N</i> one-soliton solutions with different velocities as <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(y\rightarrow \pm \infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>y</mi> <mo stretchy="false">→</mo> <mo>±</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>, where <i>y</i> is a spatial variable. Before and after each interaction, the <i>N</i> solitons pass through each other without any change in shape, velocity, while only encounter the phase shifts. Taking <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(N=2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>=</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(N=3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>=</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation> as two examples, we graphically illustrate the 2 and 3 interacting solitons through the 3D plots and density plots, which align with our asymptotic-analysis results. Our results might help people understand some localized waves in nonlinear optical fibers.</p>